Why are the water, nitrogen, carbon, and oxygen cycles important to an ecosystem?
Because they are vital for life
Water is needed by both plants and animals, availability of water impacts what species can be present in what quantities in an area.
Oxygen is equally important for life, both plants and animals need to breathe.
Carbon is used to construct the vast majority, if not all, organic molecules and compounds, also plats use it in photosynthesis.
Nitrogen is also very widely used in the construction of organic molecules.
Their cycles regulate how much water/nitrogen/carbon/oxygen there is in one ecosystem and how quickly they will be replenished over time. So the cycles regulate both the species present in an ecosystem and in what quantities, as well as the changes through time of that ecosystem (seasonally, annually, etc).