(Also spelled paperdoll. This form appears to be more correct, and Google said this (mis)spelling was more popular, so there =)
A paper doll is a doll that is actually just a picture drawn on paper that is then cut out along the edges. (There are some paper dolls that are ready cut, but most are just printed on sheet of paper and need to be cut by the user - this is part of the fun. For more mature audience, making the whole paper doll can be even more fun.) Once the thing is cut from the paper, it's a two-dimensional figure.
Typically the paper dolls consists of a lightly clothed human figure, and all sorts of paper clothes or accessories that can be worn on the figure (typically attached by folding the flaps that are left on the edges of these things).
There are also computerized paper dolls (see KiSS).
And through this computer reference, we come to another definition of paper doll: in many graphical CRPGs, the character information screen shows what is often informally known as a "paper doll", even when it is neither paper or doll, but the resemblance is striking. The character is often there unclothed, and if you equip weapons or wear clothes and armor, the paper doll gets to wear all this stuff - as does, of course, your character. Some games that I've recently played that have this feature include Ultima VII (U7 with Exult, U7SI natively...), Baldur's Gate and Morrowind, but there are tons of more...
(Could there be a link between playing with paper dolls at early age and then later stressing the importance of stylish clothing in CRPGs? People who just stare at the AC when choosing the armor miss a lot of things =)