Certain extensions — like Gmail notifiers, for example — are great when your browser is running, but can't run when it's closed. Chrome's added a new feature that will let extensions stay open, even if you don't have any open browser windows.
There aren't a ton of extensions using this feature yet, but it's fairly new. We expect that just like desktop extensions, a lot of developers will be adding this feature to their extensions very soon. Essentially, it allows you to start a process and close all your Chrome windows. The process (checking your Gmail, for instance) will stay open in your system tray, so it can keep giving you desktop notifications even when you don't have any Chrome windows open. This also allows Chrome apps to load content in the background too, so apps can actually update in real time even when they're closed. That way, when you open up their page, you don't have to wait for anything to load—all the information is right there, fully updated and ready to view.
We're pretty interested to see what developers do with this feature now that it's out. To test it out, you can check out the countdown timer app, which will send you notifications even when you've closed all your Chrome windows. Hit the link for more information.