Trophies are part of a point-based system that will rank artists, based on their participation in the platform, inside their Weekly League group. See also: "Help Article: What are Weekly Leagues?".
You can receive Trophies by each minute you're live streaming on Sessions, and also from receiving Love donated by fans. Additionally, you'll get Trophies for each individual fan that visits your stream. See also: "Help Article: How can I earn League Trophies?". Just note that, due to the weekly nature of the Weekly League, Trophies reset back to zero every week.