In order for an email to have this signature, who ever sent the email must have had access to my personal computer, and they must have known the passphrase which unlocks my private encryption key.
Hence, if you see a signature like this, you can be essentially certain that I really sent that email.
Furthermore, if you enable PGP or GnuPG encryption on your own computer, then email sent between us can be fully encrypted, secure from the prying eyes that wander the Internet.
If you use PGP or GnuPG and would like to send me encrypted email or verify my identity, my public key is available here: http://www.math.duke.edu/~adsmith/adsmith-pubkey.asc