The concept of corporations goes back to Roman times and possibly still further. The basic idea is that a group of people got together to form a venture. Normally with profit-bearing motives. The word ‘corporation’ even comes from the Latin, ‘corpus,’ meaning ‘group of people.’ Part of the idea of corporations being that the venture could live on beyond the lifespans of normal people. Corporations really caught on as imperial trade ventures spread further and further afield, growing with the globalisation and taking us to the point today where these huge entities dominate national stock markets and their corporate footprint is everywhere. Most visibly seen in the products we buy and the logos we see all the time.
In terms of the relationship between governments, corporations, and the people, the view seems to be that the government is paternalistically representing the people and that corporations are off to the side regulated and taxed by the government, and people have the choice of whether or not to transact with them. In a way, they are almost considered to be a subset of the people, in the respect that many also own shares in the corporations, either directly or through their pooled investment schemes, like pensions. Also, people believe that the government is voted in by and represents the people, and the people only.
This old-fashioned view is questionable.