What is the importance of alleles in humans and other organisms?

Alleles are alternative genes for a specific trait. Alleles can be thought of as variations of a particular gene. When an organism has two identical genes (alleles) for a trait, it is said to be homozygous and when an organism has two different genes (alleles) for a trait, it is said to be heterozygous for that trait. An example is a person who has two alleles for brown eyes and is homozygous for the trait of eye color. 

All of the alleles in an organism make up its genome. An organism's genotype is its specific set of genes while its phenotype are all of its observable traits. Due to mutation and natural selection, many loci along the DNA have various alleles. More alleles may lead to a greater variety of traits in offspring. This is particularly important because habitats on Earth are constantly changing and if a species' genes remained the same, they may not provide a selective advantage in a new environment. Thus, the species would die out.

The alleles an organism possesses may or may not confer an advantage for survival in a particular environment. However, when an organism creates gametes or sex cells through the process of meiosis, due to the law of segregation, an organism's traits determined by its genes separate from each other creating a variety of sex cells. Also, due to the law of independent assortment, gene pairs separate into gametes independent of one another assuring that a huge number of possible combinations of genes can be transmitted to the next generation.

Alleles may be dominant or recessive, incompletely dominant or co-dominant. When an organism receives its gene pairs from its parents, for every trait, based on laws of heredity, different alleles may be observed or hidden in an offspring. For instance, if a person inherits an allele to produce melanin (A) and another allele that doesn't allow melanin production (a), this individual (Aa) is heterozygous for the trait of melanin production, but will have normal pigmentation because allele (A )is dominant to allele (a). However, this individual is carrying the allele for albinism. 

To summarize, the alleles an organism possesses comprise its genotype which in turn determines its phenotype. The environment also plays a role in gene expression. Alleles are important because it is their combination within an organism that may help it to survive in a particular environment and if it is considered to be "fit" it will reproduce and perhaps pass those adaptations down to future offspring.