chiasma
If you watch paired chromosomes through a microscope during meiosis, you can see them touching at little X-shaped crossing points. Each such point is a chiasma: the physical, visible site where two homologous chromosomes have exchanged segments by crossing over. The word comes from the Greek letter chi, which looks like an X.
A chiasma forms where non-sister chromatids of paired homologs have broken and rejoined to one another. It appears during the later stages of prophase I, after pairing, and marks where genetic material has been swapped. The number and position of chiasmata vary from one cell division to the next.
Beyond marking recombination, chiasmata serve a mechanical role: they physically hold the homologous chromosomes together until they are pulled apart in meiosis I. This tension helps the chromosomes line up and separate correctly, so a failure to form at least one chiasma per chromosome pair raises the risk of mis-segregation.
Keep the terms straight: crossing over is the molecular event of exchange, while a chiasma is the visible structure that results. They refer to the same underlying recombination, seen at different scales.