Water from a cycled tank is just water. The cycling process is one that takes place in the filter and gravel. Basically, animals and decaying matter produce waste (ammonia). Ammonia is toxic to animals, but in the wild is diluted by large bodies of water. In our tanks it builds up. Thankfully there's a bacteria that "eats" ammonia, and produces nitrites as waste. Nitrites are not as toxic as ammonia, but is still not good for animals. THANKFULLY, there's another bacteria that consumes Nitrites, and produces Nitrates, which are non-toxic except in extremely high concentrations. All this bacteria grows and lives on any surface area, tank walls, floor, gravel, ornaments and filters (sponges are effective because of the large surface area). They also need oxygenated water at all times.
So to cycle a tank, you introduce ammonia (in the form of a fish or some food), and it builds up in the water. Soon, your filter and other surfaces build up a colony of the 1st bacteria. Your water will now contain nitrites. Soon the 2nd bacteria comes around to use the nitrites up. The water will now contain nitrates which you remove through water changes or is consumed by live plants. During this cycling process you must make sure that the ammonia input stays the same, otherwise the bacteria will starve and you must start again.
Basically it's building up a colony of bacteria that can handle the ammonia of all your animals without letting any build up.
