The Libravatar project is part of a movement working to give control back to people, away from centralised services and the organisations running them. It addresses a simple problem: putting a face on an email address.
By using this service, you can choose what picture to display next to the comments you leave on other people's blogs or next to your forum posts. Furthermore, if you own a domain name, you can choose to opt out of this service and run this free software on your own server, on your own terms.
If you run a website or are the author of a web application, you can use the API (or one of the available libraries) to serve these images to your users without having to worry about hosting them yourself.