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With the exception of the sex chromosomes, each pair has the gene loci in the same positions on each chromosome, and the centromere in the same position. They are not genetically identical because they will usually have different alleles (versions of a gene) at some of the loci.
The most important fact is that homologous chromosomes physically pair for meiosis, the cell division which produces the gametes. During this pairing, crossing over takes place between chromatids of each pair. This exchange of alleles means the offspring are not identical to each other, or to either parent. In other words, the process increases the genetic variation in the population.
Sex chromosomes only pair along those parts where there is similar genetic material (loci) on both members of the pair.