Depending on your desktop environment, it is possible to get notification when there is new mail.
The default implementation (which you can override) depends on the same system used for the See Bookmarks and Maildirs, in the main view and the See Modeline, and thus gives updates when there new messages compared to some “baseline”, as discussed earlier.
For now, notifications are implemented for desktop environments that support DBus-based notifications, as per Emacs’ notification sub-system See (elisp)Desktop Notifications.
You can enable mu4e’s desktop notifications (provided that you are on a
supported system) by setting mu4e-notification-support to t. If you
want tweak the details, have a look at mu4e-notification-filter and
mu4e-notification-function.