oration n.

late 14c., oratour, "an eloquent or skilled speaker; one who pleads or argues for a cause," from Anglo-French oratour (Modern French orateur) and directly from Latin orator "speaker," from ōrare "to speak, speak before a court or assembly, pray to, plead."

This is sometimes said to be  from PIE root *or- "to pronounce a ritual formula" (source also of Sanskrit aryanti "they praise," Homeric Greek are, Attic ara "prayer," Hittite ariya- "to ask the oracle," aruwai- "to revere, worship").  But according to de Vaan, the Latin word is rather from Proto-Italic *ōs- "mouth," from PIE *os- "mouth" (see oral). He writes:

The chronology of the attestations shows that 'to plead, speak openly' is the original meaning of orare .... The alternative etymology ... seems very unlikely to me: a connection with Skt. a-aryanti 'they acknowledge' and Ru. orat' 'to shout', since nothing suggests a meaning 'to shout' for the Latin verb, nor does it seem onomatopoeic.

The general meaning "public speaker," is attested from early 15c. Fem. forms were oratrice (early 15c., from Anglo-French); oratrix (mid-15c., from Latin); oratress (1580s).

c. 1600, "to pray, to plead," from Latin oratus, past participle of ōrare "speak, pray to, plead, speak before a court or assembly" (see orator). The meaning "make a formal speech, talk loftily," used humorously or contemptuously, emerged c. 1860 in American English as a back-formation of oration. Related: Orated; orating.

c. 1200, orisoun, "a prayer," especially "a set prayer that forms part of a religious service," from Anglo-French oreison, Old French oreisun (12c., Modern French oraison) "oration," from Latin orationem (nominative oratio) "speech, oration," in Church Latin "prayer, appeal to God," noun of action from past-participle stem of ōrare "to speak, pray, plead" (see orator). Etymologically, a doublet of oration.