Gunplay is the mechanics and feel of weapons in a game.
Clearly different weapon classes.
Subtle but noticeable changes between weapons within a class.
Simulates the accuracy of the weapon, the ability to hit the same place repeatedly. The better the quality of the weapon and ammunition is the better this will be.
Simulate the handling of the weapon and how easy it is to keep stable and trained on a target.
Affects the Vertical and horizontal movement of weapon when firing.
Some random stats that weapons can have.
Deploy Time - The time it takes to weapon be able to fire after switching to said weapon.
Aim Down Sight Time - Time to switch to Aim down sight.
Weapon stats can be modified by the player characters actions, abilities and weapon modifications. Two common modifiers is the stance and the movement speed of the character. If running dispersion can be much higher and if laying down sway can be lowered. How much they change can depend on each weapon so it is much harder to run and shoot a machine gun then a pistol.
Reference
The Art of First Person Animation for Destiny - 2015
Techniques for Building Aim Assist in Console Shooters - 2013