Web archiving is a series of steps that work together for an end goal: to interact with a website as it looked on the day that it was archived. There are examples of web archiving without non-replay purposes, such as data mining, but generally web archiving is a process of the separate steps of capture, storage, and replay, each using different technology.
Once all of that is captured, plus a little metadata about the site (like its title), the crawler stores everything in a WARC, or web archive file. WARCs have a limit on how much they can hold, so it usually takes multiple WARCs to store a website. Unfortunately WARC files will not automatically replay on a screen when opened, but require technology to replay them. The Archive-It replay mechanism is called Wayback.
The end result of all of these steps is the page as it looked on the day it was archived.