Unimpeachable describes someone or something that is totally, completely, without any doubt, innocent and good, like an unimpeachable role model who avoids bad influences and sketchy situations.
Impeach means "to accuse, or charge with a crime." It is a verb usually reserved for when high-ranking officials like presidents do something wrong. So, when you add the prefix un- and the suffix -able, the result is an adjective that means "not able to be accused," in other words, beyond doubt or question. If you run for public office and your past is unimpeachable, your opponents will have nothing to use against you in their advertisements.