In simplified terms, did you find everything you could have possibly found? Looking at the formula in the article, it includes the false negatives, that is, items you misclassified as negatives when you should have considered them positives. And because that happened, you didn't find them in the set, that is you "forgot them". The opposite of forgetting is... recall.

Another place this idea comes up is a search engine index. If the algo doesn't find, for a given query, documents in the index it should have (falsely classified as not matching the query), it will have lower recall.