An interesting concept. A kind of read-only webmail service with no signup.
Basically, as soon as mail is sent to email@example.com, the account "foo" is created. Anyone can then go to Mailinator's page and read the mail for account "foo"; there's no sign-up, no personal information, not even a password. Also, all mail gets deleted after a couple of hours.
They say one possible use is when you want to sign up with some service and need a temporary email address; then you typically only need it to be valid for an hour or so, long enough to check the email for the validation key or registration code or whatever but afterwards you may not care any more. So, no spam problem for you.