Platonic forms are imaginary, perfect representatives of a concept. There are lots of different types of birds. However, if we had one bird to represent the "bird-ness" of all of them, this would be the platonic form of a bird. We could also imagine a platonic form of a chair, serving as a perfect example of chairs, capturing all of their "chair-ness".

If there is a set of things, such as birds, then there is likewise a distinctive attribute uniting all the parts of this set--like their bird-ness--and the platonic form of that thing is the imaginary entity that possesses that distinctive attribute (the bird-ness) and nothing extraneous to it. For example, the platonic bird will not be red or blue, since these attributes are contingent and not definitive of bird-ness.

These things don't really exist. But they are similar to the idea of a "prototype" from cognitive science. The idea is that our brain builds up concepts through examples, for example building the concept of "bird" by seeing lots of birds; maybe all of this information is stored in a "prototype" for bird in our brains.