What is Weapon Handling?
The closest thing I've found to an official statement on it, is a developer tweet:
Handling is a single stat reflecting both recoil and gun sway. Higher numbers are better (meaning at higher numbers, the gun has less recoil and/or less sway).
What this means is that Handling will reduce the amount of sway and deviation the area gets from firing a gun (more so when firing continuously), while more Accuracy will make the initial area your gun can hit smaller.
Source