An alternative explanation is something else that could've explained the same thing. So let's say that my house is wet. One explanation is that it rained. Another alternative explanation is that some of the piping burst, or someone sprayed it down with a garden hose.
A counterexample, on the other hand, is an example that helps to disprove some statement. For example, let's say we have the statement "All swans are white." Well, if you found a black swan, that would be a counterexample proving that statement wrong. Hope this helps! Feel free to ask any further questions that you might have.
