Middle English holden, earlier halden, from Old English haldan (Anglian), healdan (West Saxon), "to contain; to grasp; to retain (liquid, etc.); to observe, fulfill (a custom, etc.); to have as one's own; to have in mind (of opinions, etc.); to possess, control, rule; to detain, lock up; to foster, cherish, keep watch over; to continue in existence or action; to keep back from action," VII strong verb (past tense heold, past participle healden), from Proto-Germanic *haldanan (source also of Old Saxon haldan, Old Frisian halda, Old Norse halda, Dutch houden, German halten "to hold," Gothic haldan "to tend").
Based on the Gothic sense (also present as a secondary sense in Old English), the verb is presumed originally in Germanic to have meant "to keep, tend, watch over" (as grazing cattle), later "to have." Ancestral sense is preserved in behold. The original past participle holden was replaced by held beginning 16c., but survives in some legal jargon and in beholden.
The modern use in the sense "lock up, keep in custody" is from 1903. Hold back in the figurative senses is from 1530s (transitive); 1570s (intransitive). To hold off is early 15c. (transitive), c. 1600 (intransitive). Hold on is early 13c. as "to maintain one's course," 1830 as "to keep one's grip on something," 1846 as an order to wait or stop.
To hold (one's) tongue "be silent" is from c. 1300. To hold (one's) own is from early 14c. To hold (someone's) hand in the figurative sense of "give moral support" is from 1935. To hold (one's) horses "be patient" is from 1842, American English; the notion is of keeping a tight grip on the reins. To have and to hold have been paired alliteratively at least since c. 1200, originally of marriage but also of real estate. To hold water in the figurative sense "be sound or consistent throughout" is from 1620s.