There are two different types of feeds, which you can access by tapping on the Instagram logo at the top of the app. The first is called Following, and this is the chronological feed of every post from every account you follow, while the other is called Favorites.
You can add up to 50 accounts as your favorites, and when choosing this feed you’ll only see their posts – also sorted chronologically.
Additionally, posts from accounts in your Favorites will show up higher in the home feed. You can make changes to this list at any time, and people will not be notified when you add or remove them.
However, neither of these new feeds can be set as the default, at least for now – you’ll need to manually select them each time you visit Instagram.