Every completed session awards XP (scaled to your level — roughly three sessions per level). Level-ups apply automatically at the 5e thresholds: more HP, new spell slots, class features, and at level 3 your subclass.
At levels 4, 8, 12, 16, and 19 you earn an Ability Score Improvement — spend it on the character sheet as +2 to one ability, +1 to two, or trade it for a feat.