Real Dictionary

register
countable noun: A register is an official list or record of people or things.
verb: If you register something, such as the name of a person who has just died or information about something you own, you have these facts recorded on an official list.
verb: If you register to do something, you put your name on an official list, in order to be able to do that thing or to receive a service.
verb: When something registers on a scale or measuring instrument, it shows on the scale or instrument. You can also say that something registers a certain amount or level on a scale or measuring instrument.

register in Accounting
noun: A register is an official list of people or things.

register in American English
a record or list of names, events, items, etc., often kept by an official appointed to do so
intransitive verb: to enter one's name or cause it to be entered in a register; enroll
noun: a book in which records of acts, events, names, etc., are kept
transitive verb: to enter or cause to be entered formally in a register

register in British English
noun: an official or formal list recording names, events, or transactions
verb: to enter or cause someone to enter (an event, person's name, ownership, etc) on a register; formally record

register in Mechanical Engineering
verb: If a mechanical part registers, it lines up with another.