Pulling is the act of starting a battle, usually by single targeting a monster out of a group to bring said group to your party, hence 'pulling' them toward you.
Pulling can be quick complicated, since it will often requires a good situational awareness as well as a good understanding of aggro range and the links between mob.
Pulling is usually done by the Tank of the instance, since the initial aggro from the pull help him consolidate threat for the reminder of the battle. However, Hunters have several abilities design to help them be good pullers, are often used as such.