"Kakebotoke" simply means "Hanging Buddha" and refers to a plaque hanging on the wall. It can also be written 懸け仏 in Japanese. Sometimes it is translated as "Hanging Disc", since it is mostly round in shape.
The votive plaque occupies a peculiar position among religious art objects because it was produced in this form only in Japan and developed in a unique way. This came into existence after the practice of enshrining Buddhist and Shintoist deities under the same roof started. The principal subject of the votive plaque were Buddhist figures (kakebotoke 懸仏); the round plaques were about 40 cm in diameter and generally hung inside a temple or a shrine. It was first called Mishootai (御神体) or the "true form of the deity", and the use of the word "Kakebotoke" seems to have started in the early Meiji period.

Votive plaques are classified in three types:
1) Round metal plates provided with one or two hooks by means of which they were suspended and on the surface of which a Buddhist figure, very often Kannon Bosatsu or Dainichi Nyorai, was engraved.
2) Round metal plates with a figure embossed, usually with an inscription of the maker and the donor on the back side.
3) Round metal plates, usually copper with gilt or silver, to which an embossed Buddhistic figure was attached.

The origin of the votive plaque seems to have been closely related to the custom in which the actual Buddhist image was reflected in a mirror. This custom was initiated by Emperor Monmu (reign 697-707) upon a suggestion in his dream by a priest, although he had planned to build a Buddhist statue.
Read a learned essay about this subject in the middle of the following HP.
http://www.tobunken.go.jp/~bijutsu/english/biken/abstract/70.html

Kakebotoke were also put up in front of a tabernakel with a secret Buddha statue (hibutsu 秘仏), which was not to be shown to the public. The votive plaques with a copy of the secret Buddha statue, sometimes up to 50 cm in diameter, became the object of veneration. Since they were stolen quite often they were later hung up high in the inner sanctuary (naijin 内陣) to prevent theft.

The custom of reflecting a Buddhist statue in a mirror for a special ritual is still alive today. Here is a mysterious story I heared in a temple in Kamakura. For special exorcistic rituals of esoteric Buddhism heated oil is poured over a Buddha statue. The statue in question was a secret statue, so the Kakebotoke substitue had to be used. Since the Kakebotoke statue of this temple had just been newly made and was quite pretty, the priest wanted to spare it this fate. He decided to reflect the statue in a mirror and poor the heated oil over the mirror. It seems the Gods accepted this sacrificial offer of a substitute with another substitute and peace returned to the poor soul for which the ritual was performed.

You want to know why this ritual had to be performed? Well, that brings us into the realm of the Ghost Stories of Lafcardio Hearn (Kwaidan, Kaidan 怪談), but here it is:
During the early Edo period, a young woman who lived in Kamakura close to this tempel had made a wish to the powerful god of this particluar temple to grant her a child. She soon gave birth to a beautiful baby boy, but died shortly after that. Since it is the custom to go back to the temple and thank the god for a granted favor (o-rei mairi お礼参り), she could not perform this ceremony and her poor soul was hanging in limbo for quite a while. Just after World War II another woman, Mrs. K. who lived close to the temple, started to have the same dream every night: A young woman appeared at her pillow, telling her the above story and asked her to have a ritual performed to pacify her soul. "If you help me, I will show my gratitude for your act!" the young woman promised. So, after consulting with the temple priest, the ritual to pacify the soul of the young mother was performed - with the hot oil on the mirror to substiture for the substitute, but the god was pacified anyway and the soul of the young woman could proceed to heaven. She appeared just one more time at the pillow of Mrs. K., thanked her again and promised to do something good for her.
Now, you ask, what good did she do for Mrs. K? That I cannot tell you here, but if you send me an Email, I might. After all, miracles happen even in our modern times.

懸仏とは
懸仏は、平安時代のいわゆる神仏習合 本地垂迹(ほんちすいじゃく)の考え方から生まれたものである。そのため明治の神仏分離の時まで、ほとんどの懸仏は神社に祀られていた。最初は神道で御神体とされていた鏡に、その神の本地仏を 毛彫(けぼり)したり朱墨で描いたりしたものであった。これら平面的なものは鏡像と呼ばれている。平安時代も半ば以降になると、尊像を半肉彫にしたものなどが作られるようになり、13世紀ごろになると丸彫に近い像を取り付けるようになる。このように立体的になったものが懸仏である。ただし懸仏の呼称は、明治時代以降になって使用されるようになったもので、それまでは銘文などからみて「御正躰」と呼ばれていたことが分かる。
残りの文書の詳しい説明をここで読んでください。
http://www.e-obs.com/heo/heodata/n158.htm

The Kakebotoke from the Cleveland Museum of Art, Cleveland, Ohio, USA.

This Kakebotoke was originally suspended by brightly colored cords from a wooden beam in a Buddhist worship hall of the late Heian period. Originally its polished bronze surface reflected the flickering light of oil and candle flames. But through the centuries of exposure to the elements and wax and oil smoke, the metal surface has acquired the rich blue-and-green patination of age and usage so admired by the Japanese. The seated figure of the universally benevolent deity, Kannon, sits on a lotus base surrounded by a double halo with flame patterns. These elements have all been cut from a sheet of bronze and delicately hammered into shape using a wood mold. The surface of the deity's figure and the individual lotus petals have been incised and carefully tooled to provide detailing of form and three-dimensional modeling.
http://www.barnard.columbia.edu/english/reinventingliteraryhistory/women/genji/votiveplaque.htm

On the following Japanese HP you can see this one and more Kakebotoke, with good details, so you should have a look at it.

伝金蔵寺懸仏
京都府加悦町指定文化財　　直径33.7ｃｍ
http://www2.nkansai.jp/off/monpaku/bunkazai/kakebotoke/kakebotoke.htm

Have a look at some more Kakebotoke in Japan on the following HPs.
懸仏のHPが幾つかあります。見てください。

Kakebotoke at Yokoyama Hachiman Shrine.

http://www2.shizuokanet.ne.jp/tenryu/jiten/bunka/bunkahtm/kakebotoke.htm

Kakebotoke form Tokuyama Town in Yamaguchi prefecture.
http://www.joho-yamaguchi.or.jp/mutsumi/tourist/tourst/kakebotoke/
http://www.city.tokuyama.yamaguchi.jp/konjaku/bunkazai/kakebotoke.html

Kitaho-shi, Treasure Hall of the Shrine Kumano Jinja.
http://www5.ocn.ne.jp/~imono01/bunka/tabunnka/kumano2/kumano2.htm

Shisha Shrine in Arai Town in Niigata, featuring Dainichi Nyorai in four forms, the last item on this HP.
http://www.city.arai.niigata.jp/culture/bunkazai/bun07.html

Important cultural property of Kazo Town in Saitama prefecture.
http://www.city.kazo.saitama.jp/SHOGAI_K/40200-11.ASP

Kakebotoke and musical plate of the Temple Koozen-ji in Ueda Town.
http://www.asama.ne.jp/t_journal/tera/17.htm

Kannon Bosatsu as Kakebotoke, Tempel Toorin-Ji in Yamato Town, Gifu.
http://www.xwns.co.jp/yamato/bunka/html/067.html

Kakebotoke of Shirahige Jinja in Sayama Town, Saitama prefecture.
http://www.city.sayama.saitama.jp/history/bunkazai/kogeihin.htm

Exhibition about Religion and Prayer in Nakanojoo Town.
http://www2.wind.ne.jp/khiroshi/look/shiryo09.html

Four important Kakebotoke at Tempel Daikyoo-Ji in Chita Town, Aichi prefecture.

http://www.city.chita.aichi.jp/kyouiku/syougai/hyu-tory/bunka/bunka/bunka16.htm

Kannon Bosatsu as Kakebotoke from the Heian period. MIHO Museum.
http://www.miho.or.jp/booth/html/imgbig/00003156.htm

On the following HP you can see a wooden figure of a Yasha demon deity, which was originally in a small shrine and is now mounted on a wooden pedestal to be worshipped as a Kakebotoke. This one is even for sale.

元来は簡素な厨子に入っていたもので、破損した厨子の背板がそのまま着いています。(取り外しも可能です。) このまま懸け仏のように鑑賞できます。
http://www3.ocn.ne.jp/~k.hosoda/108-C8Yasha.htm

Daruma as Kakebotoke だるまの懸仏
Since Kakebotoke is originally just a hanging Buddhist figure, I take the liberty to add our Daruma san to this categorie. Most of the Daruma plaques are made of wood, now even of plastic, but they still serve the purpose of being worshipped in the hope for some favor in life. So let us have a look at some Darumas hanging on my wall.
懸仏はただ壁に掛ける仏の像のことですから、達磨の壁掛けもその仲間です。昔は綺麗な木材で出来ていましたが、いまはプラスチックのものもあります。 私の壁にあるだるまの懸仏を見ましょう。

The one on the left is of beatuifully shaped wood, almost triangular. On the sides it reads: Seven times Down, Eight times Up (七転八起). The plaque is 35 cm high and 70 cm wide.
左側のほうが珍しい形の木材でできています。七転八起も書いてあります。
The one on the right is a square plaque of black wood with two Darumas in the form of a papermachee Daruma. One of them is carrying a flywhisk. The plaque is 24 cm high and 32 cm wide.
右側のほうは黒く染めた木材で、二人のだるまは張子のような形をしています。

This Daruma appears on an oval wooden plate and is very carefully carved and polished. It is 50 cm high and 35 cm wide.
次のだるまは素晴らしい彫り物で綺麗に輝いています。

This last one is a special gift from a friend, who made it of pottery after visiting my Daruma Hall. It is meant to hang at the door and greet the visitors. It is about 13 cm high and his face is quite individualistically formed. Please come and see for yourself.
最後に特別なものがあります。私の達磨堂を拝見したあとで友達は焼物としてつくりました。今入り口に懸けてあって、お客様の出迎えをしてくれます。見に来てください。

Postscript 後書き
A Daruma to hang on the wall, that discription also fits for a Daruma shop sign, so read my story about Kanban.
壁に掛けるだるまさん、それは看板のことでもあり、看板のお話も読んでください。

Latest news about Mirrors. 鏡についての最新情報
Right now there is an exhibition about "The Art of Reflection: Mirrors, Messages and Magic" at the Victoria and Albert Museum in London until 31 March 2003.
http://www.orientations.com.hk/thisiss.htm
Here are some more HPs with information about Bronze Mirrors.
http://www.asiawind.com/antiques/mirrors.htm (good explanation)
http://www.markajohnson.com/Chinabronzemirrors.html (nice pieces for sale)
Japanese Metal Art
http://www.jgc.co.jp/waza/b6_jmetal/jmetal01.htm
http://www.trocadero.com/Nipponart/items/42143/item42143.html
Korean Metal Art
http://www.hoammuseum.org/english/gallery/me_art_01_09.html
http://www.koreainfogate.com/beautykorea/cultural/cultural.asp?src=Metal&title=Metal%20Arts
http://www.tang-soo-do.org.uk/koreanart.html

You can read more about rituals of esoteric Buddhism in my German book about Buddhist Ritual Instruments of Japan 日本仏教法具の辞書, which you can order here:
珍しいドイツ語の書籍・47冊