A gamete is the organisms sex cell. In humans, female gametes are the eggs cells, and male gametes are the spermatozoon. Because of the law of segregation, each gamete carries one allele for a trait, insted of a pair.
However, during sexual reproduction the female gamete and the male gamete come together to form an embryo with the complet pair of alleles for each trait.
In summary, we have two alleles for a trait because one came from our mother and the other came from our father.