Rate of Fire (or Fire Rate) is a description of the ability of a weapon to "shoot a lot of bullets in very little time".
Numeric Rate of Fire
Every weapon has a numeric Rate of Fire. This number more or less corresponds to the amount of bullets that can be fired in 1 second. A Sniper Rifle with a 0.4 Fire Rate will fire 1 bullet every 2.5 seconds. A SMG with a Fire Rate of 4 will fire 4 bullets per second. This rate does not take into account weapons with several bullets per shot (shotguns, for example)
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 will fire several bullets in quick succession with every pull of the trigger, and then stop, rather than fire continuously as a Machine Gun would. Additionally, the given fire rate will give you no indication of how long this pause 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. The fire rate on these weapons describes the speed of individual bullets during a single burst, but not how far apart these bursts are. So 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 only tell you the rate during bursts, and not the actual rate between two bursts.