A counterexample contradicts the statement or definition you're trying to set up.
For example, if you said that 2x+3x = 7x was true for all x values, then all you need to do is try something like x = 2 to find the original equation simplifies to 10 = 14, which is false. In this case, the counterexample is x = 2 invalidating the equation 2x+3x = 7x.
