Somewhere in this long string sequence we begin finding base sequences which, when read in triplets, make sense. This is called an 'open reading frame', and it always begins with a start codon (AUG) and always ends with one of the three stop codons (UAG, etc.) We can call this open reading frame a gene IF it translates into a sensible, functional protein or is biologically active (like a binding site). Note: many do NOT; they're mutated and called pseudogenes.
On the homologous chromosome to the one we've been looking at (the one from our other parent), at the same location on the string of DNA, is an identical open reading frame. It MAY have one or two different base pairs, which MAY cause one or two amino acid substitutions. These substitutions MAY cause the protein product to express a phenotype slightly differently (blue eyes/brown eyes); therefore we can speak of it as an allele [ different variation ] of the other gene.