By using temp mail you get a free temporary disposable email. This can be used to sign up for services or promotions without giving out your real email address.
For the user it can mean less spam and advertising, and more anonymity and maybe less chance of getting hacked.
For the service provider though, it means that they have no control over users creating multiple accounts, etc. If they give out trials or free stuff, by using temp mail, a user can get unlimited emails and free stuff.