What is damage spread as it relates to Team Fortress 2?

Damage spread refers to the fact that a weapon has a spread, or range, of damage that it can deal on any given hit. By default, weapons generally have a +/-10% damage spread.

So if a weapon has 100 base damage, it might do as little as 90 (10% less than base) or as much as 110 damage (10% more than base) on hit. This amount of damage dealt is simply a random value from within the "spread".

Originally, the spread was +/-25%, but Valve eventually reduced it to only +/-10%.

Note that this isn't the only thing that affects weapon damage, there is also a damage falloff based on range for most weapons (they do less damage at greater distance).

Some servers disable damage spread because they think it makes the game more "skill-based" and more fair, since damage dealt is more consistent. This is similar to the argument used for disabling critical hits.