Routing does pretty much what it says on the label - it allows you to alter the route that the audio signals take before reaching the output stage whether that's your amp or your recording device.
In a simple setup the mixer is used as a way to input multiple sources and output them to a single destination such as your PC.
A simple use of routing would be to send the output to a reverb unit and then have the processed signal fed back into the mixer before sending the final result to the PC. This is commonly done via a dedicated Send/Return in/out on modern mixers and most allow you to adjust the individual signal levels sent from each source which is usefull in the above example if you want just a touch of reverb on, say, the bass guitar.
You may also want to route a single input such as guitar. This would allow you to play a clean signal into the mixer and then send a copy of that signal to a processor such as a distortion pedal. You then take the output from the pedal and feed it back into to a different channel on the mixer. This may seem pointless as you could just plug your guitar into the pedal and record that but it allows you to mix the clean and the distorted sounds in a very flexible way. If your mixer has multiple outputs it also allows you to keep the clean sound on a separate track which means that you could always route it back to the mixer if you decide that you want a different sound from the pedal later on. You would input the recording instead of the guitar and route that instead.
To be honest, in a small home-studio setup with a modern mixer that has Send/Return built-in, routing is not really a major issue and you're not missing out on anything vital. It would be worth your while digging around Google or better still getting a good quality up to date book on mixing if only for the extra tips that you find. It's quite interesting but it's another skill tat takes some learning which can drag you away from making music if you're not careful. (It suits me cos I'm not that good at the music anyway
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