An offer was a proposal with the intention of doing an action for or giving an object to another to be accepted or rejected. An offer typically involved the use of money for buying or selling a product or service.
In 2268, the barman of Deep Space Station K-7 offered Cyrano Jones one credit apiece for tribbles, as opposed to Jones's asking price of ten credits. He then upped his offer to two credits, then four credits, to which Jones asked "Is that an offer or a joke?" The barman replied that it was his offer and Jones replied "That's a joke." (TOS: "The Trouble with Tribbles")
In 2364, Hagon asked why Lutan was so obsessed with Lieutenant Tasha Yar over Lutan's First One Yareena who could offer him much more and owned many things and many lands. (TNG: "Code of Honor")
The Earth deep space probe Friendship 1 freely offered various cultural, scientific, and technological information to alien civilizations that it came into contact with. This was with the hope that one day Humans would stand on alien soil and extend their hands in friendship. (VOY: "Friendship One")