A corporation is usually a for-profit business organization, which is incorporated (ie. completed the process of becoming a corporation) and can act as a separate legal entity. The benefit of a corporation is that the owners (aka shareholders) can separate and protect their personal assets.
In the United States, you can establish a private corporation and keep it that way, or you can later go public. Note that there are 3 types of corporations (ie. LLC, S corporation and C corporation) but only C corporation can go public.
related links:
https://www.thebalancesmb.com/how-to-incorporate-your-small-business-in-7-steps-2951524
https://www.foxbusiness.com/features/five-reasons-why-a-small-business-should-incorporate
https://info.legalzoom.com/incorporated-mean-business-24222.html