Not opened reminders notify you when someone doesn't open an email you've sent them.
When not opened reminders are activated, you should receive a reminder email 24 hours after sending a still-unread mail that looks like this:
As you can see, in the reminder mail you have the option to change the time intervals so that, for this particular email send, for example, you can be reminded again in 24 or 48 hours to follow-up with the recipient if they´ve still not read the email.
There is also the option to disable not opened reminders, either completely or for one contact in particular:
You can disable/enable not opened reminders as well in the advanced notification settings when you go to compose a new email.