GNU project flagship product.
The program's purpose is to "produce a familiar, friendly greeting. It allows nonprogrammers to use a classic computer science tool which would otherwise be unavailable to them."
In other words, it prints out "Hello world"... and also checks your mail, making it better than the competition.
Actually, the program is intended to be a practical illustration of GNU Coding Standards. It also serves as an example of how to make a Debian package.