early 15c., periode, "a course or extent of time; a cycle of recurrence of a disease," from Old French periode (14c.) and directly from Medieval Latin periodus "recurring portion, cycle," from Latin periodus "a complete sentence," also "cycle of the Greek games," from Greek periodos "cycle, circuit, period of time," literally "a going around," from peri "around" (see peri-) + hodos "a going, traveling, journey; a way, path, road," a word of uncertain origin (see Exodus).
Sense of "repeated cycle of events" led to that of "interval of time." From 1712 as "an indefinite part of any continued state or series of events;" by 1727 as "time in which a circuit or revolution (as of a heavenly body) is made." Sense of "episode of menstruation" is by 1829, probably short for period of menstruation (1808), etc..
The meaning "dot marking end of a sentence" is recorded c. 1600, from the earlier sense of "a complete sentence, from one full stop to another," then "a full pause at the end of a sentence" (1580s). The educational sense of "portion of time set apart for a lesson" is from 1876. The sporting sense "division of a game or contest" is attested by 1898. As an adjective from 1905; period piece is attested from 1911.