What is it for and how do I get to it? It looks to be partially unplugged and my car's electronics are all bugged out.

 

i think there is more then one... but the one you probably see, is the fog light relay

 

Are there any tricks to getting back to it? I can't figure out how to drop the glovebox or its liner.

 

Look at the glovebox and you will see a little actuator on the left side, its the dampener that keeps the glovebox opening and closing gently. Then push in on the sides and pull down from the top. There are one or two tabs holding it place. From then on the glovebox drops down all the way.