In Drupal 7, you can add fields to users the same way you would a node. These fields are more flexible than the previous core profile module, and include, for example, taxonomy term references. Go to Administration » Configuration » People » Account settings and click on the tab to "Manage fields" to add fields. For additional functionality, you can use the Profiles2 module, which has a separate profile tab and private profiles.
In Drupal 6, the Content Profiles module provided additional functionality to the (now deprecated in Drupal 7) core profile module.