If you use a service that doesn't support multiple sign-in, it will default to the first account that you signed in using your browser. Google suggests to use a different browser, but you can also use Chrome's incognito mode to sign in to an additional Google account.
Another limitation is that Gmail's offline mode is disabled if you turn on multiple sign-in.
Multiple sign-in will let you open Gmail in multiple tabs, log in using different accounts and read the messages from all your accounts without opening another browser. Right now, you have to log out before logging in to a different account.