Gmail enables you to access the same account from multiple computers by logging in with your Google Account username and password. If you have set up two-step verification on your account, you must provide an additional authentication code when logging in on a new computer; this is typically sent to a registered mobile phone number.
If you're logged into the same Gmail account on two different computers simultaneously, Google will alert you to this fact with a warning message in your inbox. Select "Details" and then "Sign Out All Other Sessions" to log out of Gmail on every computer except the one you're currently using. It's worth following this "Details" link occasionally to look for activity in your Gmail account that you don't recognize, which may indicate that someone else is trying to access your email.