Wire with mysterious power
That red wire is most likely part of a 3-way switch configuration, and not connected to the light at all.  Disconnecting it would rid you of the benefit of this configuration -- i.e. both switches would have to be on for the light to turn on.  With the red wire connected, either switch can turn on the light.



(A 3-way switch is an electrician's term for a single-pole, double-throw (SPDT) switch.)