This is a function that allows you to register users you like to a favorites list. If you follow using the public settings, the new submissions of the followed users will be displayed on your top feed page. You can follow privately but in that case new submissions will not be shown on your feed.
* For pixiv Premium members, new submissions even of people you follow privately, will be displayed.
If you follow publicly, third parties can also see that you are following the user. If you follow privately, neither the other user nor the third parties can see that you are following the user.