Here is an excerpt from wikipedia about deionized water:

Deionized water is used in freshwater aquariums. Since it does not contain impurities such as copper and chlorine, it keeps fish free from diseases, as well as avoiding the build-up of algae on aquarium plants, due to its lack of phosphate and silicate. Deionized water should be re-mineralized before used in aquaria, since it also lacks many macro and micro-nutrients needed by both plants and fish.
Link to the full wiki article is here: Deionized Water.

Also, here is more info:Using Pure Water
Pure water can have specific uses in the aquarium, including:

* Topping up water lost to evaporation. This should ensure a constant hardness level in the aquarium, as only pure water evaporates, leaving behind salts, etc. This means that constantly topping up with tap water will gradually increase the hardness/mineral content of the water because pure water is being replaced with water containing a range of minerals.

* Lowering hardness (and usually pH at the same time) by mixing a percentage with your normal tap water.

* Providing a much purer source of water for your fish, which can have enormous benefits.

Note that pure sources of water must never be used alone in the aquarium. They are too pure, and contain none of the essential minerals that fish need, and also have no buffering capacity to stabilise the pH. It can either be mixed with a certain percentage of tapwater (it is possible to produce various hardness levels in this manner), or the commercially available salt mixes can be used to replenish a balanced mix of electrolytes - note that these are not the same as normal 'aquarium salt'.