MTA is indeed message transfer agent.
Most hosts on Unix run a local MTA. This enables mail to be sent notwithstanding any external server, quickly. It won't timeout, even if the local mail server is down at the time, as it uses a pipe to get sendmail to place the mail in the outgoing queue.
This is a good thing.
Some Windows servers don't use this scheme, and instead encourage direct delivery or delivery via some remote, sometimes unavailable server. This is very bad, as a temporary failure will permanently cause a mail to be lost, moreover, mail() will timeout.
Talk to your systems administrator to ensure that their MTA is either local (i.e. on the same box) or very nearby and unlikely to be down at any given time.
Local is always preferred.
Even if the mail needs to be routed via another "smart host" server, a local MTA can keep it temporarily in a queue in case that other server is down.
Mark