Rooting does not do anything other than allow you to do all the things you mentioned. Rooting is basically the same as logging in to the administrator account on a windows machine, it gives you permissions to do whatever you want to the system, in this case your phone.
Once you have rooted, then you can install apps that require root permissions. A few examples are file managers that can manipulate all the folders instead of just the sdcard folders, apps2sd apps that will allow you to install apps to your sdcard instead of your internal memory so you have tons more storage, TitaniumBackup (and others) that will allow you to backup-restore-freeze-unfreeze apps (another potential storage saver), juicedefender and tasker which if used properly can dramatically improve battery life, and a whole lot more.
When you are ready, rooting also gives you the ability to install a custom recovery and rom. Depending upon the rom, many of the apps the features I listed above are built in, saving you time setting them up, and more room on your phone's memory.