OK so this is how I see it !

Like Noticingthemistake said, EQ (at the mixing desk) in the live or recording environment is all about cutting through the mix and not cluttering up your frequencies fighting with other instruments / vocals.

When you mix stuff down there will be several areas where the frequency's generated by one instruments overlap with another. This can lead to the masking of those frequencies / muddying up the mix making individual instruments difficult to hear. One way to combat this is to turn down the overlapping frequencies.

Usually your mids will be in the bit that doesn't over lap !

These tweaks in EQ at the desk are quite subtle relative the the big mid scoops associated with say a death metal sound relative to a midsey blues sound made on your amp (which are fundamental to "your" guitar sound).