Each user runs a separate blog connected to their username. For example, here's mine MasterRussian.NET - MasterAdmin - Blogs

But when you click the Blogs tab, you will see the stream of the latest blog posts from all users.

The index of member blogs is found here MasterRussian.NET - Member Blogs - Blogs
Just click the username to follow a particular user. The number of your blog entries (if you have any) is also shown under your avatar. I have one at the moment.

These blogs work as REAL blogs. You can customize your style to fit your personal preferences, control permissions & privacy, view blog statistics, edit title and description, etc. To make changes go to Blog Settings in Control panel.