In Forsaken World, dungeons (aka instances) are short raids with a team of players all working together towards a common goal. The rewards for doing these instances can be anything from large amounts of experience for your character and pet, rare items, money, titles, etc. Most of these can only be performed a limited number of times per day, and some can only be entered at specific times during the day or week.
Most of them can be applied to by the Team Apply menu (pressing T to open it), with either a pre-made party or solo to get randomly grouped with other solo joiners. This will also cover Events, which are timed incidents that don't usually get done in a team but still somewhat apply. These are done by going to the required map area at certain times of the day and applying. Check the daily events screen (press U to open it) to see the times for these various events.
There are a number of dungeons available for play in Forsaken World. Below is a list of those currently available.