Ultimate Frisbee (otherwise known as Ultimate, Flatball, or just Frisbee) is a fast-paced non-contact sport, where each team is aiming to catch a disc in their opponent's endzone. There is no running while holding a disc and the other team will try to block your passes from player to player - if they do, then they get the disc!
The game works by one team having possession of the disc and passing it between their players, with possession at the start being given to the team who were scored against last point, performed by the other team throwing the disc in the form of "the pull" to them. If the team loses control of the disc at any point (by the disc going out, touching the ground without a player having control of the disc or the opposing team getting the disc) then possession switches to the other team. Catching a disc in the opponents endzone causes gameplay to be reset.
When a person has possession of the disc, the defending team (team without possession) are allowed one player (the mark) within 3 metres of said person. They must be at least a discs distance from the mark and are unable to touch them. The defensive player counts from 1 to 10 in seconds
(saying: "STALLING 1... 2...") - if the defender says any part of the "ten", then possession turns over. If the defender is counting too fast, the person with the disc can object by yelling "FAST COUNT" and the mark has to drop the count by two. The marker is also not allowed to intentionally touch the defender. There are various other infractions possible, but these are the main ones.
A person with a disc must also have a foot fixed on the ground - their pivot foot. This is usually the opposite side of their throwing hand (so a right-handed player's pivot foot would be their left foot). Their other foot is able to move freely. If a defening player sees an offensive player in violation of this rule, they can yell "TRAVEL" and the player must take the disc back to where it was. Note that if a player catches a disc with momentum, they're allowed a reasonable amount of stopping distance.
These are the main rules, but there are plenty more you'll learn by playing. If you also like reading, then you can read the complete set of rules here