A pull refers to the opening act of combat when mobs are pulled from their location to the character or group. Not all fights start with a pull, but it can be very helpful in instances and in certain crowded areas. The point of a pull is to move mobs, and therefore the fight itself, to a safer location away from other mobs. This is extremely useful when you are fighting mobs that run when they get low on health. If you pull those mobs away from surrounding ones, you have more time to kill it before it goes and gets its friends.
Pulling is done by a class with a ranged ability. In instances, the tank will often pull simply so that they have the initial aggro of all of the mobs that will be pulled. In instances mobs are almost always linked so this gives the rest of the party time to apply Crowd Control without having to worry about the mob beating on them. At level 70 hunters get a spell called Misdirection that makes pulling and setting the aggro on the tank very easy.
While regular pulling is always done by a ranged class, there is a concept called body pulling that paladins, who have no innate ranged pulling ability (in general, Blood Elves can pull mobs with a mana bar), employ. What this refers to is the act of running up to a mob or group of mobs just to the point of aggro, gaining aggro (usually by judging a seal) and then backing up slowly to drag the mobs to a safer area. In most cases this isn't the ideal method but it can work well.
Another style of pull is the Line of Light (LoS) pull. This is typically used when the mob or group of mobs has a ranged ability that will make it difficult to simply have them run back to you. Backing up out of range of their ability can work, but it's hardly ideal so using LoS is very handy. What this means is that damage is done to the group of mobs and then the person who has their initial aggro will then run around a corner or another obstacle. This breaks line of sight and causes the mobs to reposition themselves to regain that line. It's important that no one else in the group who is in line of sight damages the mobs causing them to not follow the line of sight of the puller around the obstacle.