Let’s say that I have a gmail address: firstname.lastname@example.org
Now if I am signing up for a newsletter at XYZ Corp. I can register with the email address email@example.com You can put in any extra alphanumeric information after the plus sign and it still gets delivered to firstname.lastname@example.org. Furthermore you can apply a filter in Gmail to process the email a certain way based on the email address that you signed you for (email@example.com).
One handy use of this feature is to track where emails are coming from so if you started to get spammed for instance you will know which address was passed onto a third party.