What is the role of the hiring manager?

They are the manager you would report to. They will primarily determine if your skills and background are suitable and also asses you personally to see if you "fit in". The recruiter makes an initial assessment on these items, but also determines your eligibility to be hired legally, runs the background check etc.

The hiring manager is the person who will make the decision on who gets hired for the position. They are often the person the new hire would report to as well. The recruiter has basically no say in the actual hiring decision, they simply identify candidates, do some initial screening, and then forward the candidates to the hiring manager. While you want to make a good impression on the recruiter, if the hiring manager doesn’t like you for the job, you won’t get it,  o matter what the recruiter thinks of you.

A hiring manager is the person who is tasked with hiring this employee.

Usually but no always the hiring manager is also the employee's manager when they start working for the company.  However, it's not uncommon for the hiring manager to be a level or two above the employee.

Hiring managers role is to fire people only. Never hire them, goddamn idiot.