You can't verify (with enough accuracy to rely on) if an email actually exists using just a single PHP method. You can send an email to that account, but even that alone won't verify the account exists (see below). You can, at least, verify it's at least formatted like one
if(filter_var($email, FILTER_VALIDATE_EMAIL)) {
//Email is valid
}
You can add another check if you want. Parse the domain out and then run checkdnsrr
if(checkdnsrr($domain)) {
// Domain at least has an MX record, necessary to receive email
}
Many people get to this point and are still unconvinced there's not some hidden method out there. Here are some notes for you to consider if you're bound and determined to validate email:
Spammers also know the "connection trick" (where you start to send an email and rely on the server to bounce back at that point). One of the other answers links to this library which has this caveat
Some mail servers will silently reject the test message, to prevent spammers from checking against their users' emails and filter the valid emails, so this function might not work properly with all mail servers.
In other words, if there's an invalid address you might not get an invalid address response. In fact, virtually all mail servers come with an option to accept all incoming mail (here's how to do it with Postfix). The answer linking to the validation library neglects to mention that caveat.
Spam blacklists. They blacklist by IP address and if your server is constantly doing verification connections you run the risk of winding up on Spamhaus or another block list. If you get blacklisted, what good does it do you to validate the email address?
If it's really that important to verify an email address, the accepted way is to force the user to respond to an email. Send them a full email with a link they have to click to be verified. It's not spammy, and you're guaranteed that any responses have a valid address.