Imagine you have a bunch of blocks, and you lay them out like a square. You have one row of one block, then another row of one block, then another row of one block. You keep going until you have a square made of blocks.
Now, if you count how many blocks you used, and that number is a perfect square, like 4, 9, 16, 25, etc., then that number is called a square number!
So, a square number is just a number that is made when you take a bunch of blocks and arrange them into a square shape, and the number of blocks you used is a perfect square.