Refers to one's spouse's parents, i.e., father-in-law and mother-in-law together. This term is formal and somewhat dated; in modern Japanese, 義理の両親 or 義父母 are more common.
Living with one's parents-in-law was once the norm.
Compound of 舅 (father-in-law) and 姑 (mother-in-law). The reading きゅうこ is the on'yomi of both characters. The exact historical derivation is uncertain, but the term has been used in formal contexts.