Animals depend on plants for both energy and nutrients. By contrast, not all plants need animals. Many flowering plants, however, depend on animals to assist them in reproduction and animals can benefit plants in other ways as well.
Flowering plants or angiosperms propagate by means of sexual reproduction. Pollen grains from one flower produce sperm that will fertilise eggs produced by another (or sometimes even by the same) flower. As part of this process, flowers need a way to transport pollen from one flower to another.
Some flowering plants are pollinated by wind; many others, however, are pollinated by animals like bees or insects. These flowers need animals to assist them in reproduction, since they can't transfer pollen from one flower to another by themselves. If a species cannot reproduce, it cannot survive, so these species depend on animals for reproduction.
In many ecosystems, herbivores graze on plants that might otherwise outcompete other plants in the ecosystem. By doing so, the herbivores contribute to the survival of certain plant species. Some plants also enjoy mutualistic relationships with animals where both parties benefit -- the most notable example being swollen thorn acacias. These unusual trees provide shelter and food for certain species of ants; in return, the ants aggressively attack competing plants and herbivores which might otherwise feed on the tree.