The site is more popular than Facebook among users under the age of 25, apparently because it's not about attracting a great deal of attention, not about getting pageviews, but about sharing with just a few friends.
Whereas Facebook is a service that encourages connecting with large numbers of people, Tumblr has a notoriously poor search interface, making it more private. Privacy, of course, is an issue that Facebook is notoriously bad at. This makes Tumblr similar to an updated version of what MySpace was before it was nearly destroyed by Facebook and rebaptised itself as a music-sharing site. Although, arguably Tumblr is most similar in culture to LiveJournal.