When securities are sold to the public (or even to the private), that's an offering.
An IPO? An offering. A secondary sale of 15 million shares from the founder, 19 months after the company was public? An offering. A sale of 22% of a startup to a venture capitalist for $3 million? That's an offering. The burning of tissues and the sperm of a righteous man to ward off spirits? Yep, that's an offering too but, uh, way less lucrative for banks.