The DNA "words" (or genes) which make up the chromosomes are collectively called the genotype of the organism. Conversely, the organism's phenotype is the outward expression of its genotype -- how it looks, thinks, acts. (A phenotypic trait may be, for example, having blonde hair.)
Since there are 64 possible combinations of bases in a codon (43 for you mathematically-oriented folks) and only 20 amino acids used as the "building blocks" of proteins, you can see that in most cases there is more than one codon which can specify a particular amino acid. Thus two organisms may possess different codons in a particular gene, yet generate the same protein product from it and thus express the same phenotypic trait. This is called having different alleles (or "forms") of a gene. Additionally, the two organisms' genes may be different enough that the amino acid sequence of the resulting proteins is slightly different, yet functionally in the body the proteins serve the same purpose. Example: we all have blood, but 45% of us are type O, and the remainder are type A, B, or AB. The organisms in the example also have different alleles of the blood-type gene.
Chromosomes occur in pairs, one contributed by the mother, and the other contributed by the father. If, for a given trait, you have identical alleles on both chromosomes, you are said to be homozygous for that gene (or called a homozygote). If you have two different alleles, you are heterozygous. Many times only one allele will express itself in your phenotype. This is called the dominant allele. The unexpressed allele is recessive. You can pass it along to your offspring, but you yourself will not show it as an outwardly visible trait.