An assist appears to be a word that contributed to a conversion. Meaning, the keyword was searched for, the searcher clicks on your ad, sees your site, but then deceides to continue shopping. After a couple of queries, he clicks on your ad again; perhaps this time while searching under a different term. Now the searcher buys. What happens is that the initial word searched gets an assist & the converting term gets the conversion. The same term could qualify for both the assist & conversion. It's a bit more info on how you get conversions.