Stacking is the act of pulling a neutral creep camp, usually not towards the lane, at such a time that the camp is empty at the XX:00 minute mark. If the camp (and a specific surrounding region, known as the spawn zone) is empty at the XX:00 mark new creeps will spawn thus increasing the number of creeps in a camp. Once additional creeps have been allowed to spawn the camp is "stacked." The challenge with stacking is to pull the camp at the correct time. The creeps do not only have to clear the actual camp they are in, but also clear the camps corresponding spawn zone which differs from camp to camp.
To stack a jungle camp simply draw the aggression of the creeps around XX:53 to XX:55 (exact timing varies slightly between camps), then run in a direction that will put you and the creeps outside of the "spawn zone" at the minute mark.
A "spawn zone" is the area associated with a jungle camp which no hero, creep units, or wards may be in at the new minute mark - XX:00 - for new neutrals to spawn in the camp. The areas vary in size and knowing which ways to pull the creeps is a vital part of playing the jungle, 4th, or 5th role.
Reasons for stacking
Pulling the lane
By pulling a stacked camp into the lane a support can draw the aggro of the lane creeps onto the neutral jungle creeps, pulling them out of the lane and into the forest. This also works for camps that have not been stacked, but stacked camps have the benefit of killing the entire creep wave while a non-stacked camp will only kill one or two of the creeps.
Pulling the lane is a good way for supports to ensure good farm for their carry while denying the opposing carry the farm and gaining quicker levels for the support. Lane pulling is a very important part of the laning phase, especially in a defensive Trilane.
Securing farm for the carry
At the end of the laning phase, when a carry will start moving into the jungle and/or ancients to farm, stacking the camps whenever possible is a vital part of gameplay. This gives the team carry more farm from the stacked camps thus putting him closer to the farm he needs to be effective.
Tactics against stacking
Playing against a support that constantly stacks and pulls can deny a lot of farm from a lane.
By placing a ward inside the spawn zone of the creep camp closest to the lane (the one used for pulling) you prevent neutral creeps from spawning there. With the current cost of wards at only 75 gold, this is something which is definitely worth it if the other team plans on stacking and pulling.