This phrase refers to someone trying to escape something something by climbing up a wall. It is not known when it was first used. Seriously, no amount of Googling yielded any results. The phrase today means to be annoyed, irritated, be driven to irrationality, etc. Here are a couple of examples of things that drive ME up the wall...

Every morning I drive our redheads to school.  We bicker over the radio stations, discuss homework, I get to hear about this person or that person and the most recent drama, sometimes I have to lay down a "law", I stop and get them treats every so often if we leave on time, and we sing along to the Disney station when nothing else is on.  For 30 minutes every day the redheads and I are captive to one another - some days we are all quiet, other days we are all clamoring to be heard above the other.  On these drives I have had some great discussions with them - individually and all together.  Some days I groan, we all do actually, about the drive but really every day I am more than happy to have this time in the car with my teenage redheads. These years are scary and wonderful for all of us and these morning drives give us all a measure of comfort I think.