Typically, with a non-admin account, you can't modify anything outside of that account's Home folder. This usually means you can't install new applications or change certain system preferences when logged into that acount. (You can put applications in your Home folder, which are then only available when logged into that account.) In general, this is a safer way to work, because you can only screw up your own account, not the entire system.
If you do need to quickly install an application or change a system setting, you can usually "authenticate" temporarily with the admin's username and password for that one task.