A corporation is legally recognized as a person and singular legal entity within the confines of the law, independent of any specific individual who may have started it. Corporations are started and maintained through legal registration and periodic upkeep, and have tax reporting responsibilities within the region in which they are registered.
Organizations can be publicly traded (and thus publicly owned) or privately held, as well as for profit or non profit. In the United States, a corporation is generally considered a larger business organization, though non-profits can still be similarly registered. Generally speaking, corporations interact with the broader economy through operations, profits, and taxes.
Corporations are, in theory, owned and controlled by members and shareholders. To simplify this logic a bit, if a company is owned equally by 5 different people, then each individual owns 20% of the value of the overall organization. As a result, ownership has a significant capital component. Organizations such as credit unions and cooperatives function in a slightly different manner, where each additional member of the project may own equal shares regardless of capital inputs.
While larger, publicly traded organizations may be owned by hundreds of thousands of shareholders, it is common practice for members to elect a board of directors to oversee the actual running of the organization (two boards are elected in some countries: a managerial board and a supervisory board). The respective boards will oversee typical operations of the firm, and ensure that the best interests of the community and the owners are being upheld.
Organizations are held accountable for their actions, just as individuals would be. As a result, organizations can be brought to court on various charges and convicted of criminal offenses. Organizations can also be dissolved for a wide variety of reasons including insolvency, bankruptcy, monopoly, and a wide variety of other failures to operate profitably and/or ethically.
The individuals within an organization, granted it is a limited liability organization, are somewhat insulated from the broader failings of the organization. This means that debts being taken out on behalf of the organization are not the liability of the individuals working there, but instead a liability of the legal entity that is called the corporation.
How to Incorporate
It's worth noting what is traditionally required of an organization to become a corporation. In the United States, each state is different, but the following are common denominators:
Business purpose (general and, sometimes, specific)