Rate of Fire (or Fire Rate) is a weapon stat, and represents how fast a weapon will shoot when the trigger is pulled.
Numeric Rate of Fire
Every weapon has a numeric Rate of Fire. This is roughly the number of times the weapon can be fired in 1 second. For example, a Sniper Rifle with a 0.4 Fire Rate will fire once every 2.5 seconds. An SMG with a Fire Rate of 4 will fire 4 times per second.
Semi Automatic vs Fully Automatic
A Fully Automatic weapon will re-fire as soon as possible, so long as you keep your finger on your trigger. In this sense, it will make full use of its rate of fire.
A Semi-Automatic weapon will only fire a shot when you pull the trigger. This will give it an overall slightly slower Rate of Fire then its numeric capacity, as you will always fire a split second after the weapon has fired.
It is possible to fire as fast as a semi-automatic weapon will allow by firing, releasing the fire button and then pressing and holding it before the next shot can be fired. This will fire the next shot on the earliest possible frame. This pattern can be repeated until the magazine is empty.
Weapons with burst fire have a very misleading fire rate. These weapons fire several bullets in quick succession with each pull of the trigger, rather than fire continuously while the trigger is held down, as a Machine Gun would. The given fire rate describes how quickly shots will be fired during a single burst, but it provides no indication of how long the pause between bursts will last.
Assault Rifles are a typical example of this burst fire discrepancy. They will fire in short bursts of (usually) 3 bullets, and then stop for an amount of time. Even though an Assault Rifle may have a fire rate of 10, if it can only fire a burst every 1 second, its true fire rate will actually be 3.3. Unfortunately, there is no way to know this 'burst fire rate' but to equip the weapon and try it.
This is true of any weapon with "increase burst fire count", such as some machine pistols. The rate of fire will apply only during bursts, and gives no indication of the actual time between two bursts.