It's an excellent way of sharing music, and a very good way of bring the anti-DRM stance into an arena where people discuss music.
This page explains it well enough: http://www.last.fm/help/
"
Last.fm is the flagship product from the team that designed the Audioscrobbler system, a music engine based on a massive collection of
Music Profiles.
Each music profile belongs to one person, and describes their taste in
music. Last.fm uses these music profiles to make personalized
recommendations, match you up with people who like similar music, and
generate custom radio stations for each person."
I've been using it for a week or so now and it's very good