Alleles are the DNA sequence(s) on chromosomes that code for the amino acid sequence in the protein(s) that will catalyze the metabolic sequences (for instance development) that result in a specific trait, usually referred to as a phenotype.
Sexually reproducing organisms (humans) are diploid 2N, so there are two allele sequences for each inherited trait: one from a mother and one from a father.
The alleles eventually inherited by the offspring of reproducing adults have a chance of being affected by 1) mutation 2) a crossing-over event during meiosis I prophase or 3) a chromosomal defect.
Also, the expression of genes is often governed by transcription and translation factors that result in a “patched together” mRNA strand and thus a final amino acid sequence derived from several loci on the gene’s DNA sequence. Plus, many traits are the result of an enzyme “cocktail” from several alleles that collaborate to catalyze the metabolic processes involved in producing the phenotypic outcome for a specific trait.
Last, the alleles inherited may be DOMINANT or recessive or co-dominant or incompletely dominant etc….
In Population genetics, allele frequencies can be assessed using the Hardy-Weinberg equation p + q = 1 where p represents a dominant allele and q represents the recessive allele.