You will see on this website, and please try it, that depending on the device everything moves around or is responsive to the width of the browser window and the natural boundary to this is a small mobile phone. Adjust the width of your browser and you'll see this in action.
This is generally fine for most sites, but a mobile site shouldn't really be bloated with a lot of options which are frankly only suitable on a desktop or perhaps a tablet device. This is where you can, and we might say that you should, consider a separate mobile site as a little sister to your main desktop site.
Another very important reason for having a mobile-only site is that the user experience is completely different. For starters, people are using their fingers and not a mouse, buttons should be bold and easy to tap and most important of all it should be very simple to use. A desktop site may have lots of features which are quite honestly very difficult to manage on a phone.