Fingerboards are small skateboards, less than 10 cm long but shaped exactly like the 'normal' ones. All sorts of tiny accessories (e.g. wheels, deck bolts) are available as well.
Although they don't have any particular use as a training device, they seem fun to play with for teenage (wannabe) skaters. They are also a lot cheaper than their bigger brothers.
The best known producer of fingerboards at the moment is
Tech Deck (http://www.techdeck.com/).