Expertise is an attribute that decreases the chance that melee attacks made by the player will be dodged or parried by 0.25%. Also, some classes and races gain an additional bonus to their Expertise rating.
Different from weapon skill, expertise is not limited to a specific weapon type. The only exception to this is the racial bonus which only receives the +5 expertise bonus when a weapon of that class is equipped.
The terms expertise and expertise rating are also different in their use. A player's "Expertise Rating" is gained from their equipped items and for every 3.92 expertise rating gained, 1 "Expertise" is added at level 70. Expertise is usually gained from talents however, and for each 1 point of expertise you reduce your chance to be dodged/parried by 0.25%. So, with this in mind, you would need an expertise rating of 15.68 at 70 to reduce your chance to be dodged or parried by just 1%.
Expertise is used several different ways on a tank. For starters, it's used to reduce avoidance and it increases threat generation. And secondly, because some mobs can attack faster after a parry, a higher expertise rating will reduce the total damage the tank takes by reducing that parry chance.
Melee DPS will also benefit from a high expertise rating. With enough expertise, melee classes are also able to attack their target from the front without being dodged or parried.