Platonic concepts are those which are discussed in the works of Plato, the pre-Christian Greek philosopher. These writings are usually framed as records of philosophical exchanges between various Greek citizens and Socrates, Plato's mentor.

Concepts or ideas attributable to Plato are Platonic, whereas those which are attributable to Socrates are Socratic.

Are you asking about everything Plato ever did or are you referring to platonic forms?

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I'd suggest reading Plato's allegory of the cave and then coming back and asking more specific questions.

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.