The root "nym" comes from the Greek onoma, a name. We use the term nym to identify many classes of words.  When an Internet searcher speaks of "nyms" they are generally referring to sets of words that improve query formation by providing precise control over keyword selection.

How can understanding nyms empower my search?

Part of any good search strategy is the careful selection of keywords.  Understanding how hypernyms and hyponyms will affect your search puts real power into your hands.  As you build a query, be aware that use of nyms will narrow or broaden your search.  This knowledge helps you form an effective query.