There are a lot of ways to transfer files to a server. Transmit is the best designed, most intuitive of these options.
If you’re building a website or transferring large files onto or from a server, you’ll need some kind of FTP program. These apps allow you to interface with your server, which in turn allows you to build websites and things of that nature.
That’s what I use FTP software for, primarily: website building. There are many ways to build websites without having to muddle your way through FTP these days — WordPress allows you to do it almost entirely through a browser, while companies like SquareSpace allow you to do so without even needing your own separate hosting plan — but I’m oldschool. I like the freedom to manually move things around and edit the PHP files directly, which can come in handy when something goes wrong, or if you simply want to see why something is futzing up on the front-end and can’t get satisfaction through the browser interface.
Not everyone will need this program, and it’s only available for Apple operating systems, but if you do build website (or intend to) and use Mac OS, it’s an intuitive, powerful, and very good-looking option.
Filezilla (free FTP software)(but ugh, so ugly)
CuteFTP (Windows-based FTP software)