The Featured Studios section on the Front Page shows studios that the Scratch Team has deemed interesting enough to feature.
Before October of 2015, only four studios were shown. In October of 2015 the Scratch Website was redesigned and the number of featured studios at a time was changed to five.
The Featured Studios section is the second row from the top.
Similar to the Featured Projects, you can suggest your studio to be featured in the "Propose Projects to be Featured" topic. Unlike projects, you can suggest your own studios to be featured. 
In the 1.x website, before the release of 2.0, there was an analogous list in the sidebar, called "Featured Galleries". It only showed 3 galleries at a time.