SMTP = Simple Mail Transfer Protocol.
An SMTP server is a server that PHP connects to in order to deliver emails you generate. Most hosts are running a Unix-type operating system, most likely one configured with an SMTP daemon. This is why "localhost" is a common value for the SMTP server.
If your host instructed you to use a different SMTP server (or if you're testing a PHP application in a development environment, e.g. your own computer at home), then you'd have to point PHP to this server. Most residential ISP's that provide an SMTP server for you to use will also require SMTP authentication - this ensures that only you can connect and send mail through their servers, not some random spamming bot.