what is pollination in green plants and its benefits

Pollination:  The transfer of pollen from the anthers of a flower to the stigma of the same flower or of another flower.  Pollination is a prerequisite for fertilization: the fusion of nuclei from the pollen grain with nuclei in the ovule.  Fertilization allows the flower to develop seeds.
Some flowers will develop seeds as a result of self-pollination, when pollen and pistil are from the same plant, often (but not always) from the same flower.    Other plants require cross-pollination:  pollen and pistil must be from different plants.

Most plants need help moving pollen from one flower to the pistil of another.  Wind moves the pollen for some plants such as grasses like corn.  Animal pollinators move pollen for many other flowering plants.

Pollinator:  An animal that moves pollen from the anthers to the stigmas of flowers, thus effecting pollination.  Animals that are known to be good pollinators of flowers include bees, butterflies, hummingbirds, moths, some flies, some wasps, and nectar feeding bats.  

What are the benefits?  Plants benefit from pollinators because the movement of pollen allows them to reproduce by setting seeds.  However, pollinators don't know or care that the plant benefits.  They pollinate to get nectar and/or pollen from flowers to meet their energy requirements and to produce offspring.  In the economy of nature, the pollinators provide an important service to flowering plants, while the plants pay with food for the pollinators and their offspring.