From school, I remember a very important rule: first you need to pour the water and then the acid (when you need to mix them) not vice-versa. This is because otherwise the aсid becomes very hot and splashing may happen.
So, why does it get hotter when water is poured into it? What reaction takes place?
This is mostly the case for sulfuric acid. Commercially available sulfuric acid is dense (~1.8 g/ml) and when water is added, it may not mix. In this case a layer of hot weak acid solution is formed, which boils and sprays around. When acid is poured into water, it flows down the flask and mixes much better, so no boiling occurs.
The reason this occurs is due to the large amount of energy released in the hydration reaction of sulfuric acid ions. Do not believe that heat comes from dissociation, as the dissociation of acids, bases, and salts always consumes energy. The energy is released from subsequent hydration, and the release may be high, especially if $\ce{H+}$ or $\ce{OH-}$ ions are hydrated.
This happens with strong acids and bases. Strong means the acid almost complete dissociates into ions; e.g. $\ce{HCl}$ to $\ce{H+}$ and $\ce{Cl-}$. When the dissociation occurs, it releases a great deal of heat (i.e. exothermic) because of the subsequent hydration of $\ce{H+}$ to $\ce{H3O+}$, as the other comments have indicated. The reason you add acid to water is that if you add water to acid, the first drop of water reacts immediately, and the heat might be high enough to boil the water instantly, which could spray acid out of the container.
This is more a problem with thermal mass. Sulfuric acid releases a lot of thermal energy when water is introduced to typical stock sulfuric acid which is about 90% acid by weight. When dilution is performed, a small mass of the acid is combined with a much larger mass of water.
If the acid mass is in the receiving flask, there is initially a small mass of acid and water as the dilution is started. The energy released will heat the low mass mixture, with four joules of energy heating up one gram of the mixture by one degree Celsius. If there isn't much mass, then the temperature change is dramatic and can easily cause the solution to boil, throwing droplets of concentrated sulfuric acid in the air.
Sulfuric acid is extremely dangerous. It is intensely hygroscopic and will readily dehydrate carbohydrates and proteins by removing oxygens and hydrogens to make water molecules. This process will destroy the carbohydrates and proteins, including the materials that make up your skin and muscle. Concentrated sulfuric acid has disfigured many people who have been unlucky enough to come in contact with it. Even when sulfuric acid is diluted the proper way, adding the acid to a volume of water can still result in an extremely hot mixture that might even boil.
Good practice involves using a receiving flask that can contain a splashing acid water mixture, such as an Erlenmeyer flask, and even chilling the mixture during the dilution. A splash shield can also be placed between the worker and the dilution mixture and it could be done in a fume hood. Heavy neoprene lab gloves, as well as eye protection, are recommended. Students in introductory chemistry classes rarely perform this dilution procedure, because of the high likelihood of accidents.
A large amount of heat is released when strong acids like sulfuric acid and HCl are mixed with water. First, adding more acid releases more heat, as it is exothermic.
If you add water to acid it forms an extremely concentrated solution of acid initially. So much heat is released that the solution may boil very violently, splashing concentrated acid out of the container and all this because the reaction is exothermic.
On the other hand, adding acid to water, the solution that forms is very dilute and the small amount of heat released is not enough to vaporize it. So it is always safer to add acid to water, and not water to acid.
