Home is just a basic, minimal configuration allowed version. Get this version if all you do is install applications/games and surf the web.
Pro allows you to modify computer policies, enable remote desktop and other things. Most of which are geared towards server environments.
-> If your job allows BYOD (Bring your own device) and requires you join the work domain (should be required), you'll need this version (Though not many allow this to begin with).
-> If you have kids and want to take the time to learn to further lock things down, this will help. (Group Policies / Security Policies)
-> If you ever want to access you computer from somewhere outside of your house, this helps (Although there are other methods that work with Home edition, such as LogMeIn or TeamViewer, but I prefer the built-in method).
EDIT: Cleaned things up a bit.