There are a few things which make flexible electronics possible. First of all on the hole they are polymer based… eg, conductive plastics… This gives them flexibility, we can therefore also use a flexible substrate, the base that the electronics are placed on.
The electronic materials is also soluble, that means that these materials can be applied as a liquid, such as ink jet printing methods. With a flexible substrate this allows for radical new manufacturing of electronics using methods such as reel to reel printing. This method is already well understood in different sectors of manufacturing and it will not be too difficult to transfer it to this area.
I hope this helps and give you a bit of background,