You get administrative access to the operating system. Some things can't be done without it. Like uninstalling system apps (the bloatware the carrier puts on the phone). Like ... well, search
rooted android apps
and you'll see all the things you can do if the phone is rooted.
I'd guess that 99.99% of the people running Android phones have absolutely no reason to root their phones, since a lot of what you can do when rooted, you can also do, even it it takes a few more presses, when not rooted.
Techies, OTOH - well, we like to be able to run the phone on the bare metal, so the phone gets rooted and we have a dozen ROMs or so that we keep flashing in and out. Like a dragster who tries a new carb tat may knock a faction of a second off his 0-60 time.
But for the average user it accomplishes only two things - it voids ALL warranties on the phone (like if the plastic cracks, it's not covered) and it gives you a good chance to turn that $500 phone into an inefficient door stop.