I am studying proofs in discrete math and I ran into this statement that "If 3 cannot divide "q" there will be a remainder of 1 or 2". I know that this is some pretty basic stuff but I am having a hard time to catch the concept of remainders.

What exactly is the definition of a remainder?

Can I conclude from this statement that if "4" cannot divide "q" there will be a remainder of 1,2 or 3?

Thanks