@scottalanmiller said:
What does Drush do? What requirements does it have that keep it from getting installed?
Drush is a CLI tool for Drupal. You can pretty much manage your whole site with it. But you need root access (or sudo).
If you update Drupal manually on shared hosting you pretty much have to back up the whole site, redownload the new Drupal version, reupload your sites folder (where all your info is), change the DB settings file, and chmod it.
With drush you type drush up drupal and you're done.
Or if you want to update everything (modules and themes also) type drush up
It's more of a pain with shared hosting to do all of that also.