crossing over
Picture two matching ropes laid side by side; you cut both at the same spot and tie each cut end to the other rope. Crossing over does this with chromosomes: during meiosis, two paired homologous chromosomes physically break and swap matching segments, so each ends up carrying a mix of material that used to be on the other.
This happens in prophase of meiosis I, after homologous chromosomes have paired up closely (synapsis). The points where the swap occurs become visible under a microscope as X-shaped junctions called chiasmata. Because the exchanged segments are equivalent stretches of the same chromosome, gene order is preserved while allele combinations change.
Crossing over is the molecular engine of genetic recombination. It breaks up the original parental groupings of alleles and creates new ones, which is why siblings inherit different blends of their grandparents' versions of genes. The frequency of crossing over between two genes also underlies the mapping of genes along chromosomes.
Crossing over occurs between non-sister chromatids of a homologous pair, not between sister chromatids (which are identical). Normally the exchange is equal and at matching positions; rare unequal crossing over, between mismatched sites, can delete or duplicate genes.