A tetrad is a pair of homologous chromosomes, each comprising 2 sister chromatids, for a total of 4 chromatids. This is the starting point of meiosis. In anaphase 1 of meiosis, the homologs separate from each other. In anaphase 2, the sister chromatids of each homolog separate.
The synaptonemal complex is a complex of proteins that physically hold the two homologous chromosomes together. While they are “hugging,” so to speak, crossing over of genetic material takes place, typically at one or more locations along the length of the chromosomes. These locations can look like a letter X under the microscope, earning them the name chiasmata (plural) or chiasma (singular).