Final answer:
Crossing over occurs during prophase I of meiosis, where genetic material is exchanged between homologous chromosomes, resulting in genetically diverse gametes.
Step-by-step explanation:
Homologous chromosomes undergo crossing over during prophase I of meiosis. This is a critical phase of meiosis I where the nuclear envelope begins to break down, chromosomes condense, and a spindle forms. Moreover, it is only during prophase I that homologous chromosomes pair up uniquely.
Crossing over involves the exchange of genetic material between homologous chromosomes and leads to new combinations of genes on each chromosome, a process also known as recombination. This process is vital for genetic diversity and is unique to meiosis I. It also ensures that during anaphase I, when the bivalent chromosomes separate, new genetic combinations are possible, significantly contributing to the variation found in gametes.