Genshin Impact starts pretty slowly, so it'll take a little while before you unlock certain core features. The biggest thing you'll want to focus on is leveling up your Adventure Rank (AR). Like I just explained, most everything you do will contribute some experience toward it, so don't fret too much about how you're leveling up.

Here's a quick rundown of some major features and what AR you need to be to access them:

AR 8: Ley Line Blossoms (a kind of world boss)
AR 12: More Ley Line Blossoms and daily missions
AR 14: Expeditions that let you send unused characters out for resources
AR 16: Multiplayer co-op
AR 20: Spiral Abyss, a massive, multi-floor dungeon, and the battle pass for extra loot
AR 22 and 27: More dungeons (called Domains)