One of the main features of Genshin Impact are the plentiful domains/dungeons, which are standalone instances where you have to fight specific monsters and bosses or solve small puzzels to unlock EXP, new items and useful materials. Every domain/dungeon can be unlocked once you have completed a certain pre-quest or reached the minimum level requirement.
Most puzzles require certain element mechanics to solve them with as little as possible damage. So always read the dungeon description carefully and chose your team wisely. Setting up a party with the recommended elements can save you alot of time.
At the current state there are not puzzle domains to solve. All Co-Op Domains are full combat instance levels.
Each Domain entry will cost you 20 Resin. This system is known from other games as a stamina access system. You can instant recharge it by spending Fragile Resin, which can be claimed as a reward in the World Rank system or buying the weekly package from the in-game store.
All regular Domains can be entered as up to a 4-player party.
Enemies will scale on HP and shield strength but not on output damage. So you can utilize simultaneous elemental reactions to keep enemies busy.
The only Domain which cannot be entered as a party is Stormterrors Lair.