In Windows Vista, an administrator password is just the password to an account (yours or someone else's) that allows access at the administrator level.
The actual "Administrator" account in Windows Vista is often disabled but if not, can obviously also be used.
There are lots of individual reasons you might need an administrator password in Windows Vista but usually it'll be to perform some kind of advanced action.
If you're trying to login to the actual "Administrator" account, try leaving the password blank. In other words, just press Enter when asked for the password.
Enter your own password. The account you use every day could be an account with administrator access.
Try to guess your administrator password. If your account is configured as an administrator but you've forgotten the password, you might be able to guess the Vista admin password.
Have another person who uses your computer enter his or her password. If there are other users that have accounts on your Windows Vista computer, one of them might be an administrator.
If so, that other user can grant you administrator privileges after logging in.
Recover the admin password using a Windows password recovery tool. One of these free password recovery tools could recover or reset your Vista administrator password.
Note: Some Windows password recovery tools in that list also have the ability to add administrator privileges to standard Windows Vista user accounts. This could be valuable if you know your account's password but it's not setup as an administrator. Some of the programs can also enable accounts - like the actual "Administrator" account.
Perform a clean install of Windows Vista. This type of installation will completely remove Windows Vista from your PC and install it again from scratch, removing all your data in the process.
Please don't attempt this extreme solution unless you absolutely have to. For example, if you need an admin password to access diagnostic tools and this is your last effort to save your PC, a clean install will work because you'll have an opportunity to setup a new account from scratch during Windows Vista setup.
Looking for your administrator password but you don't have Windows Vista? See How To Find Windows Administrator Passwords for instructions tailored for other Windows operating systems.