What determines a bullet's grouping?

[CISJoshB]

What, other than recoil, the user's unsteady hands and gravity, causes bullets to impact different places on the target?

 

[mfb]

Things which might influence the bullet:
- Air conditions (wind, ...)
- Imperfections in the ammunition
- maybe the temperature in the weapon (as it can expand parts of it), which can increase during its use

Gravity should be the same for all bullets.

 

[CISJoshB]

Why is velocity often said to increase accuracy? Because it can go further before being blown off course or dropped?

 

[mfb]

Higher velocity -> shorter flight time for the same distance.
It reduces the time for air and gravity (and probably other effects) to modify the path.