Pollination is the transfer of pollen from the anthers to the stigma. The pollen may be transferred from the anthers to the stigma of the same, or different flowers.
The pollen contains the male gametes (sperm) of plant. The pollen is transferred from the anthers where it is produced to the stigma where it germinates forming a pollen tube. The pollen tube then transfers the male gametes to the female gamete (egg cell) which is contained inside the ovules. Once the sperm reaches the egg cell it fuses with it to form a zygote and fertilisation takes place.
If you want to understand why pollination is such a critical part of a plant's life cycle it is necessary to understand the life cycle of the flower plant in great detail.