Unix was conceived with the idea of multi-user systems in mind, so it has a permission framework to allow different users to use a machine with different levels of access and to share files.
Each file is owned on different levels by both an individual user and a group.
A group is an arbitrary list of users. Each user also has a group that includes only them.
Files can have three main types of permissions: read, write, and execute. Each of these permissions can be allowed or denied for three groups of users: the user that owns the file, the groups that owns the file, and other users.
The most obvious use of group ownership might be to have a file that you can edit, a select group of other people can read but not change it, and people outside that group can't even read it.
Seeing a file's metadata (who owns it, what its permissions are, how big it is, et cetera) doesn't require any of these permissions.
Changing a file's permissions requires being the individual owner. Being a group owner and having all three permission bits won't do.
The permission bits set on a file are also called its mode, hence the name of the
chmodcommand: change mode.
For directories, the read bit by itself only lets you see the names of the files inside. To go into the directory, or to do anything else to its contents - even just to use the permissions you have on the files - you need execute permission on the directory.
Basically, you can think of a directory as a program that gives you access to the files inside. Take that analogy with a grain of salt, though.
There are some weird interactions possible. For example, if you have execute permission but not read permission on a directory,
you can go into it with
cd, but you can't see anything inside it. If you have permissions on some of the contents,
you can do whatever you're allowed to do on those files, but can't even see that they're there with
Write permission on a directory does nothing without execute permission. With both, you can add new files to the directory or rename files in it, and also delete files in it (see The Sticky Bit below).
Sometimes, it might look like seeing the contents of a directory requires execute permission. This is because if you have
ls colored output enabled (which your shell probably does by default),
ls is actually doing that by
statting every file it finds.
stat tells it what type of file it is and what the access mode is, so
it can color it bold blue if it's a directory, red if it's executable, et cetera. But of course
stating a file
needs execute permission on the directory that contains it.
The setuid and setgid bits
There are a couple of special flags that can be set on files. ('Flag' here means a boolean (either on or off) piece of data.)
The setuid bit (set user ID) is a way of giving users a permission they wouldn't normally have, but only through a specific
program. If you have execute permission on a setuid file, you'll be able to run that program with the permissions of the user who
owns it. This is how commands like
su work in Unix: the executable is owned by root, but
anyone can execute it and the program's internal logic will see about granting them root access. No one can change
su though - no one has write permission - so you couldn't, say, change the program to do something destructive and
then take advantage of its setuid feature to elevate your privileges.
The setgid bit works the same way, but gives you the permissions of the group that owns the file.
The sticky bit
The sticky bit is the most complicated. Normally, write permission on a directory lets you delete anything inside it, even something you don't own and don't have write permission to. The sticky bit changes this rule so that even if you own the directory you can't delete or rename stuff inside it that you don't own.
On regular files, the sticky bit has no effect.
You can find more information about this stuff in the manual pages
Information about the user accounts and groups on the system is stored in the files
/etc/passwd doesn't actually have the passwords; those are in a different file that only
root can read, like
/etc/master.passwd if you're on FreeBSD (I think it's different on Linux).)
passwd(5) and the like for more info on how those files are formatted.