A profile is a biographical page for a person in your unit (faculty, staff, etc.). These are legacy types that are deprecated, as we now recommend you plan to use the GT Scholar project, instead. The community has not yet created a feature/module to connect these to Drupal sites yet.
At the most basic, a feed is a list of content from Mercury. Feeds let you organize any content from Mercury — your own and others' — and then display it on other web sites. The two most common types of content you will find in feeds are either events or news.