Quests are Tasks and Missions given from NPCs to Players. In return for finishing Quests, you receive In-Game Money, Crate-Keys, Special Items and more. Quests can have multiple Parts and form Questlines with smaller quests inside.

Free Quests

To receive Daily and Weekly Quests, visit the NPCs at /warp village and accept quests respectively to the Dimensions you have unlocked. You can receive 5 Daily-Quests every day, and 5 Weekly Quests every week. These Quests usually reward you with Money and Crate-Keys.
To view all of your active Quests, check out your Questboard at /quests

Buyable Quests

Since releases 1.19 and 1.20 it's possible to use the /buyquest command to purchase quests infinitely.
It's possible to buy daily quests by default, whilst the ability to buy weekly quests gets unlocked with the Ranger rank.
These quests are buyable infinitely but you cannot hold more than one buyquest at a time per type.