Your badges can be found on your profile, under the section titled "Badges and Frames".

Badges can be earned in many places! Each month an exclusive badge can be earned in the monthly pass, badges can also be earned in parties and by mastering playlists.

To display a badge, all you have to do is tap the badge you want to display and then tap "default".

Badges can also be levelled up once you've accumulated a number of the same badge.