A caller is a team member who provides strategy decisions and acts as team leader during a match. The caller will designate targets, count down to spikes, decide whether to advance or retreat, split the team into groups, and basically runs things.
The caller is usually a melee class (if the team includes any melee) because they are the classes that have to actually get up to the targets that are being spiked. Therefore, they are usually the ones who decide when they can actually spike someone.
The caller is almost always the team leader.