Explained here are concepts to make your understanding of these issues skyrocket. Well, that's what we'll try to do, anyway. In Unix, every user is a member of a group. For example, when you add a user, that user is normally a member of the group users . Almost all users are members of the group users .
Notable exceptions are normally members of wheel or admin , the administrative groups.
The same holds true for groups and group IDs. I'll use these abbreviations from here on out. Each file in the directory structure is owned by a user. Each user is owned by a group. To keep things flexible, each file is also owned by a group - by default it's owned by the group that owns the user.