A mixer map let's you create a control surface in your host sequencer to drive, erm, a mixer, like the Mackie Control.
I think Cubase has a stock mixer map for the Mackie Control, so you just have to load it. Creating a mixer map is a pain though, so I avoid it like the plague.
I recently got a Novation Remote SL 25 with their Automap software, where most plugins are mapped to the controllers on the device when you load them. In this case, Novation has done all the work for me. I like this.
Drum maps let you create templates that you can use to load settings for your drums where you can define what note triggers what drum sound, the name, the default velocity, the default note length, etc.
I think this may come in handy if you work your drums a certain way all the time, but I just opt to loading sounds into Drumrack in Live and taking it from there. I think drum maps were pretty handy when you used an external sampler. Setting it up right one time would save you the hassle of saying, pad 1 is the kick, pad 2 is the snare, and so on.