Homologous chromosomes are pair of chromosomes, one inherited from father and other inherited from mother, that contain the same genes (but might have different alleles of those genes). Those chromosomes pair up during meiosis (prophase I), where they exchange genetic material during the process of crossing-over. This is where genetic recombination occurs and as a result, daughter cell contains different combinations of maternally and paternally parts.
Chiasmata is a point where two non-sister chromatids belonging to homologous chromosomes touch.