A perfect square is an integer that equals some integer squared. For example, 16=42, so 16 is a perfect square. But 15 is not because 15 is not an integer.
You can check if n is a perfect square by computing n and checking if it's an integer. In code: take the floor of the square root, square it, and see if you get n back.
Perfect squares appear in number theory problems, geometry (area calculations), and dynamic programming. Let me show you a problem that uses this concept.