Register has several meanings, but one of the most common is to write down or record officially. Like registering your car with the DMV and registering for classes at the beginning of a semester.
Someone needs to register all the ways you can use the word register: As a noun it means the actual book that you record things in. But a register is also the range of sound your voice can make, and that thing the checkout lady uses to ring up your grocery bill. As a verb, register means to mark down officially or sign up, but also to show emotion: if cats and dogs rain from the sky, your face will likely register a look of disbelief.