A corporation is a business entity which has filed articles of incorporation. Unlike a Sole Proprietorship or a Partnership, a corporation is a legal entity that is separate from its owners.
They are often referred to as C-corporations or C-corps, to distinguish them from S-corps, which are named after the subchapter which describes them in the law (though technically speaking, S-corps are corporations, too).
Filing for a legal status as a corporation is more costly and burdensome than other types of businesses. A corporation will have to file Articles of Incorporation with the Secretary of State, and may have to establish a board of directors and issue stock certificates to the owners.
The owners participate in the profits but are not held responsible for any legal liabilities, aside from criminal wrongdoing. Owners can treat themselves as employees for tax purposes, generally. A company can be privately held or publicly traded.
A private placement offering of equity shares to sophisticated investors can help raise capital for the business, but it must follow the rules of SEC Regulation D. If a company decides to start issuing shares to the public they issue an Initial Public Offering (IPO) after receiving approval from the SEC.
Generally, the company will seek the assistance of an underwriting firm – which are generally large investment banks – to decide what type of stock to offer, the starting price, and the date of initial offering.
The money raised from the IPO is all the capital that the company will receive from their issued shares — the rest of the trading in the open market is to the benefit or detriment of the buyers and sellers only.
The owners of common shares of stock have voting rights when board member elections come up. Corporations are largely defined by this characteristic amalgamation of ownership and the ability of the entity to outlive any one owner or partner.