When you log in (give a name to getty) you identify yourself to the computer. It then runs a program called (naturally enough) login, which takes your password and checks to see if you are authorized to be using the machine. If you aren't, your login attempt will be rejected. If you are, login does a few housekeeping things and then starts up a command interpreter, the shell. (Yes, getty and login could be one program. They're separate for historical reasons not worth going into here.)
Here's a bit more about what the system does before giving you a shell (you'll need to know this later when we talk about file permissions). You identify yourself with a login name and password. That login name is looked up in a file called /etc/passwd, which is a sequence of lines each describing a user account.
One of these fields is an encrypted version of the account password (sometimes the encrypted fields are actually kept in a second /etc/shadow file with tighter permissions; this makes password cracking harder). What you enter as an account password is encrypted in exactly the same way, and the login program checks to see if they match. The security of this method depends on the fact that, while it's easy to go from your clear password to the encrypted version, the reverse is very hard. Thus, even if someone can see the encrypted version of your password, they can't use your account. (It also means that if you forget your password, there's no way to recover it, only to change it to something else you choose.)
Once you have successfully logged in, you get all the privileges associated with the individual account you are using. You may also be recognized as part of a group. A group is a named collection of users set up by the system administrator. Groups can have privileges independently of their members’ privileges. A user can be a member of multiple groups. (For details about how Unix privileges work, see the section below on permissions.)
(Note that although you will normally refer to users and groups by name, they are actually stored internally as numeric IDs. The password file maps your account name to a user ID; the /etc/group file maps group names to numeric group IDs. Commands that deal with accounts and groups do the translation automatically.)
Your account entry also contains your home directory, the place in the Unix file system where your personal files will live. Finally, your account entry also sets your shell, the command interpreter that login will start up to accept your commmands.