An initial public offering (IPO), referred to simply as an "offering" or "flotation", is when a company (called the issuer) issues common stock or shares to the public for the first time. They are often issued by smaller, younger companies seeking capital to expand, but can also be done by large privately owned companies looking to become publicly traded
Due to the increased scrutiny, public companies can usually get better rates when they issue debt.
As long as there is market demand, a public company can always issue more stock. Thus, mergers and acquisitions are easier to do because stock can be issued as part of the deal.
Trading in the open markets means liquidity. This makes it possible to implement things like employee stock ownership plans, which help to attract top talent.