Answer:
Pollen grains are small (male) plant cells, usually yellow in color produced by flowers. For a seed to form pollen has to be transfered from the male anthers to the female stamen part of a plant flower. Some plants get insects to carry the pollen from flower to flower for them (rewarding the insect with nectar for doing this). Other species of plant rely on the wind to blow their pollen around. These wind pollinated plants (most grasses and some trees) need to produce vast quantities of pollen to ensure that some of it gets to a female flower and this can cause problems for people that are allergic to pollen, it gives them hay fever.
In order to warn people who suffer from hay fever when to take their medicines, the weather service measure the number of pollen grains in the air at regular intervals and publish this as the pollen count.