The ground wire is essential unless you have a well grounded antenna bracket with no paint between the metal. All antennas require 2 parts to complete the wave radiation properly or you will have bad SWR. One side is the radiator and the other is the ground side. The ground side is essential to properly send out your radio wave. On a mag mount the cars roof metal becomes the ground through inductance(kind of like an electrical transformer's windings) therefore not needing a ground and the wider the magnet base the better it will ground. On a hard mount the either you must mount it bare metal to bare metal or add a ground wire going to something that's bare metal like under a bolt somewhere on the chassis.

SWR is standing wave ratio - basically if you don't have a "perfect antenna" you will have a reflected wave which means that instead of the radiation leaving the antenna it will come back down the ground side and back into your radio ( can even come out through your hand mic if you have a metal button on the back) and could possibly cause RF burns. Even worse than the unpleasant burning sensation your signal wont get out well!!!

There are varying degrees of SWR so you need a meter to read it. You want to see 1:1 match which means that for everything you sent out all of it left the antenna. if it's less it would read 2:1, 3:1 or worse. ANything under 2:1 is considered ok. i.e. 1.5:1

My antenna wouldn't read under 3:1 without the ground so I added it as my bracket didn't have a built in one.