A nerf is a change to the rules of a computer game that weakens a certain object or ability. A nerf is usually applied during a patch and can affect a wide variety of things. The most common occurrences tend to be abilities that are determined too strong. Cost, damage, healing, range, effects and a wide variety of different mechanics to a certain ability or object could be targeted by a nerf.
The opposite of a nerf would be a buff.
A good example would be if ability X did Z damage and was deemed too powerful a patch will lower Z damage to Y damage.