Pretty much every mail client like Outlook and Mac Mail provides the ability to display a notification on the screen when a new email arrives.
In a web browser however that doesn't come automatically. Gmail makes it easy though, so if you want to read your Gmail account in the web browser window there's a setting on the general page that allows you to turn on notifications. Then when you receive an e-mail even if the browser window is minimized you'll see a notification on the screen telling you that a new e-mail has arrived.
if you're using a mail client and the web browser the same time you probably don't want notifications from both because double notification for each email may become irritating.
On the other hand if you are only using the browser this is a very useful tool.