Temporary or Disposable email addresses are offered by services which allow you to register a "throw away" email address, and that very easy. When creating a mail address their server might show a fixed domain (the part after the "@") or lets you pick one from their list. The server then creates a seemingly random local part (the letters or numbers before the "@") for that domain and activates it instantly. Any email sent there shows up usually with no delay.
These disposable email addresses might be used to sign up for services you don't want to expose a more important email address such as Facebook, Twitter or one-shop occasions where you want to avoid receiving spam later. Unfortunately many services, especially Facebook, do not allow many of the temporary email addresses, so it can be a pain to finally find one they accept.
There are different kind of services. Some expire the email address after an hour, may be a day with no way to change this. Other service don't let them expire at all. So have a closer look if you think you need an email for longer than that time after the address expires.