When you're at a restaurant with a group of people, the restaurant staff will refer to the group as a "party". For example, the check might include a note at the bottom which says:
A 15% service charge is automatically included for parties of 6 or more.
This means that the tip is included in the bill if your group has 6 or more people.
A group of people can also be called a "party" on a tour, at a hotel, or at an amusement park.