An allele is defined as one form out of two of a gene that can either be inherited or achieved through a mutation. Each human has two alleles, one for each chromosome (humans have two of each chromosome). There are only two possible traits for an allele: positive or negative. Since everyone has two alleles, an individual with two positive alleles is termed homozygous dominant, an individual with one positive and one negative allele is termed heterozygous, and an individual with two negative alleles is termed homozygous recessive.
The way I was first taught to understand alleles was the blue eye/brown eye problem. Blue eyes are known to be recessive, brown eyes are known to be dominant. To have blue eyes, a person must be homozygous recessive or the trait will not be shown. Even one copy of the dominant allele gives rise to that trait. So that means if you have one recessive allele and one dominant allele, you will have brown eyes. If you have two copies of the dominant allele, you will still have brown eyes.
A lot of times this isn't the case with traits, multiple alleles are necessary for one single trait (like skin color).
PS: This is my first post for the A to Z Challenge, good luck to everyone who is participating!