Counter used for numbered periods in a school timetable, e.g. 1限目 (first period), 2限目 (second period).
First period is math class.
Third period was canceled today.
時間目 and 限目 both label a numbered class period (3時間目 = 3限目), but 限目 is heard more in everyday spoken Japanese while 時間目 is the standard term used in official school timetables.
限目 adds 目 to mark the ordinal explicitly (2限目), while 限 alone (2限) is the shorter, more common way students refer to the same period.
Compound of 限 (limit, period) and 目 (ordinal suffix). The exact historical derivation is uncertain, but the combination naturally yields 'nth period'.