Underdeep other players characters turn up inside the dungeon as you explore, and that encounter is the whole multiplayer feature: a scoreboard, a friend system, randomly meeting other players in the dungeon and exchanging gifts. There is no PvP, no partying, and no way to group up with other people.
Underdeep other players characters: what actually happens
Your character meets other players' characters inside the dungeon as it runs, and the Meets counter on the character panel tracks how many encounters you have had. In practice the asynchronous multiplayer is light: a scoreboard, a friend system, and randomly meeting other players in the dungeon to exchange gifts.
The gameplay is automating your character's behaviour rather than playing actively alongside other people, so the encounters are a side feature rather than a second game mode. You can customise your dialogue and behaviour settings before setting out, which is what you use to decide how your character responds to a stranger.
Gifts turn into friend points
The encounter is also how the friend system starts: you can send a friend request while you are meeting a player, or afterwards by clicking their name in the run summary. Gifts exchanged during these meetings are the source of friend points, and the friend points guide covers what those points and the login bonus are worth.
Why the game needs a connection
Because the other characters are real players' creations arriving asynchronously, the game needs an internet connection to run. That is the stated reason the demo will not launch without network access, and it is also why there is no offline progression.
No party, no PvP
You cannot group up with other players and you cannot fight them. If you are coming from a party-based narrative CRPG and want to know exactly what that changes, the Baldur's Gate 3 comparison lays it out side by side.