The basic processes of meiosis and fertilization serves to shuffle chromosomes. But a single chromosome is a long string of DNA that codes for a number of different genes in sequence. If a shuffling of chromosomes was all that occurred, genes on the same chromosome would remain forever linked.
However careful observations and genetic analyses revealed that nature has another trick — CROSSING OVER. An arm of one chromosome literally crosses over and is swapped with with the arm of its partner chromosome as seen in the following video animations. Note that the crossing over can occur at any point along the length of the neighboring chromosomes.
(In these videos, you can ignore the technical jargon. The key feature for students to note is that the process results in differing gametes. The second of the two videos below illustrates the significance of the crossing over process in more detail.) Please post questions.