A cour is a unit of television production. Exactly how large a unit varies from country to country and industry to industry. In anime, a cour is typically one calendar quarter (three months). This equates to roughly 12 weekly episodes, though a cour may run slightly longer or slightly shorter.
Basically, a cour is roughly equivalent to a calendar season, but the term ‘season’ could be easily confused with Western-style production units, where ‘season’ now typically refers to a year’s worth of broadcast (often split between two calendar years).