If you’re trying to look up the term universal family, my recommendation is to *not* to use the search string “universal family” in Google.

**Update.** In the comments, Matt Heath points out that this post is already in the top ten for “universal family”, which means that I can be the change I want to see in the world. A universal family is basically a fine moduli space. A common example of a universal family is a classifying space in algebraic topology. A description of universal families in the context of elliptic curves can be found in Dan Edidin’s What Is… A Stack?