Dry ammo storage is the easiest way to keep ammo stored. You just take the shells and put them on a rack, with no special precautions taken to keep them safe. These would commonly explode if hit by another tank's shell, which would almost always destroy the tank and its crew.
Wet ammo storage is like dry, but the casing the ammo is in is protected by an ethylene-glycol-water mixture - basically fancy antifreeze. This makes it so that when a shell hits it, a resulting fire and detonation of the shells would not happen as often. This saved many tank crews after their ammo racks were hit, so this is a relatively important change made to tanks.
Blowout panels are the modern way of dealing with ammo explosions. It is simple, above or to the side of the ammo storage, you put a weaker panel that could easily be blown off by the pressure of the ammo exploding, so if the ammo did explode, the explosion would just be sent out of the tank, leaving the crew scared, but fine for the most part. The only problem with this is that after the ammo explodes there is no ammo left, so the tank has to retreat (unless it has ammo in a different place) with not gun to defend itself with.