An ad ignorantium or appeal to ignorance is a form of fallacy that assumes something to be true because it hasn't been proven false.
The argument generally looks like this:
The claim P has never been proven to be false.
Therefore, P is true.
Ad ignorantium arguments are invalid because the fact that a claim has not been proven false does not mean that it is not false.
Nobody was ever able to prove that Ben stole the cookies.
Therefore, Ben is innocent.
In this example, the problem is clear: just because nobody could prove that Ben was the thief, it does not follow that he is innocent. It is possible that others failed to prove Ben's guilt because they did not try hard enough, or because Ben left no evidence.