I made a quick PHP script on my server containing a call to mail() and started testing it. The html page always loads instantly, so I assume that means the PHP containing the call to mail() is finished executing. However, the emails sent from mail() are only ever being received every 10-20 minutes after the call. Why the delay? Does mail() trigger external programs? (the emails are being sent to a gmail email account if that's relevant)
The behavior you are seeing has nothing to do with PHP's
mail() function. Instead, it is the SMTP mail server which PHP hands off the message to, which is taking time to deliver. That service is known as a mail transport agent, or MTA.
There are lots of potential reasons it won't be delivered immediately. Possibly, the delay you see is greylisting on the receiving server, meaning that the receiving mail server refuses to accept the message until the sending server (which your PHP script handed it to) tries a few times to resend it. Well-behaved MTA's will retry failed send attempts, but spam servers often don't, making this a simple but effective method for cutting down spam.
It could even be as simple as a long queue of messages on the SMTP server waiting to be sent, whereby yours are waiting in line. (Really greylisting is more probable though)
Most important to remember though is that email is not intended to be instantaneous and therefore never guaranteed to be instantaneous. In the past decade or so we've gotten accustomed by and large to email being delivered really quickly, but you can never promise quick delivery.