c. 1200, "fact of being born;" mid-13c., "act of giving birth, a bringing forth by the mother, childbirth," sometimes in Middle English also "conception;" also "that which is born, offspring, child;" from a Scandinavian source such as Old Norse *byrðr (replacing cognate Old English gebyrd "birth, descent, race; offspring; nature; fate"), from Proto-Germanic *gaburthis (source also of Old Frisian berd, Old Saxon giburd, Dutch geboorte, Old High German giburt, German geburt, Gothic gabaurþs), from PIE *bhrto past participle of root *bher- (1) "to carry; to bear children" (compare bear (v.)).
Suffix -th is for "process" (as in bath, death). Meaning "condition into which a person is born, lineage, descent" is from c. 1200 (also in the Old English word). In reference to non-living things, "any coming into existence" is from 1610s. Birth control is from 1914; birth certificate is from 1842.