What does "bank" mean in these context?
bank, n. "a set or series of similar things, especially electrical or electronic devices, grouped together in rows."  Examples: bank of switches, bank of lights.  

Basically, 'bank' means 'group' or 'set'.  When it comes to things like memory and registers, there is usually some addressing related connotation, perhaps having to switch between different register banks, or having different register banks for different modes of operation, or having different banks of RAM within a chip, etc.