What does it mean when, we say that the earth's water is always moving, or part of a cycle?

Water is always moving around, unless it is trapped in ice for long periods of time.

The water cycle represents how water is always moving.

Water accumulates in clouds and then falls to the earth as rain. It accumulates in bodies of water and eventually evaporates back IP into the atmosphere. Water is always moving, whether it be inside animals, plants, or stuck in ice.

Water is continuously moving from phase to phase through the water cycle. If the water is in the form of liquid in a lake, it is either moving with water currents or freezing or evaporating, which moves it to the next part of the cycle. If it's in the form of clouds, more and more water is being collected from water that evaporated below until the clouds are dense enough it begins to rain or hail (depending on the temperature), where it returns to the ground and changes into a liquid state again. The water cycle never ends, it just keeps repeating over and over again. That's what is meant by water is always moving.