The background investigation phase pretty much consists of verifying all the info you put down on your SF-86/eQIP and any additional investigation needed to resolve any discrepancies that might be uncovered.
The adjudicator then looks at all the information collected and decides if you can be granted a security clearance, based on the adjudicative guidelines (see google for more info ). Most people have some issue (minor or not-so-minor), and then the adjudicator has to make a decision whether it is so serious that you cannot be granted a clearance. During this process they may request additional info.
That’s the process in a nutshell. I’m sure I’ve left some stuff out and there’s probably some better descriptions on line but there you have it.