The Google Operating System blog explains it this way.
When you enable this feature, the most significant change is that you’ll see a new drop-down next to your email address in Gmail and other supported Google products. Click on the drop-down and you can sign in to a new Google Account without signing out from the previous account.
There is also some information from the Google Help Center that only served to confuse me.
“If you use multiple sign-in, the first account you sign in to will be your default account. If you visit other Google products that don’t support multiple accounts after you’ve signed in, you will automatically sign in to your default account for that product. If you sign out of any Google product while signed in to any account, you will be signed out of all your Google Accounts at once.”
That ‘clarification’ was Google’s version of the old “you know that I know, that he knows that I know” in my opinion, but what do I know?
The bottom line is that you will not be forced to sign in to each new account every time. That should keep things easier to manage.
Now you can read your messages from two or more Gmail accounts by opening Gmail in multiple tabs.
Of course, nothing is perfect.
There are some known issues related to multiple sign-in: this feature is not available on mobile devices, Google Calendar’s gadget doesn’t work properly in Gmail, you can no longer use offline Gmail and offline Google Calendar and the “note in Reader” bookmarklet only works for the default account.
Just more evidence that Google is trying to make your life a little easier so you won’t get a wandering eye and be tempted to test what someone else is doing.