Hi Andy
The reason for using a balanced connection between guitar and mixer rather than a standard jack is that the balanced connection will be less susceptible to noise picked up in the lead. For a relatively short lead this may not be a problem but if you're running the cable from stage to a mixer position front of house, this could become an issue. A DI box converts the 2 conductor (centre core and shield) guitar lead into a 3 conductor (2 core and shield) lead. The principle is that as the signals carried by the 2 inner conductors are the same but out of phase with each other, any noise induced in the cable is counteracted by the same but out of phase noise in the other core conductor - more here - http://en.wikipedia.org/wiki/Balanced_audio. Another DI box could be used at the mixer end to unbalance the balanced feed if it has to be connected to a standard jack input.
A good quality (passive which uses a transformer or active which relies on electronics) DI box should make as little difference as possible to the sound
Roger