From the SE blog post currently linked at the top of meta:
Imagine you’ve just gotten on an elevator with a friendly stranger. You have precisely one floor to describe your community to them. What would you say? The elevator pitch is a brief sentence that describes what your site is about. Every word counts!
Once decided, it can be sliced and diced to form:
- the tagline
- the motto
- the blurb under the logo
- a convenience redirect “nickname” for the site
- perhaps eventually the domain name in some form
For more detail see: Stack Exchange Naming for Dummies