Invalid proof is when two statements are given that don't make a complete proof. A proof is a way to show how two statements are related to each other. For example, if I wanted to show that 2+2 = 4, I could show that if I add two numbers together, and then add two more, I will get the same answer, 4. That is an example of a valid proof.
Invalid proof is when I try to show those two statements, but I don't show the relationship between them. For example, if I just say that 2+2 = 4 and then say that Tom says 4 is correct, that does not show a relationship between the two statements, so it's an invalid proof.