In diploid organisms, chromosomes are paired such that each set of genes has effectively two copies. For example, in humans, we have 46 chromosomes, but each chromosome is paired with one very similar to it.
These chromosomes are called homologous chromosomes. Because these chromosomes have a number of similar or same characteristics, they match up with each other. In fact, cells even recognize that they are the same in the process of meiosis, as homologous chromosomes are paired and separated from each other in a normal division!
Even though these chromosomes are homologous, they are not necessarily the same! In fact, the differences in these homologous chromosomes are the cause for differing alleles for the same gene and, when combined, that person's genotype. For example, a person may have one gene coding for an lack of taste for phenylthiocarbamide while the other gene may code for the taste. At this point, we start to consider genetics and which allele is dominant, and which of the homologous chromosomes will express the protein causing the expected phenotype. In our example, the dominant trait is to be able to taste phenylthiocarbamide, which is very bitter if you have that trait!