During the rise of the industrial revolution in England during the 18th century, rich promoters were making massive profits off the massive rise of industrial businesses. This promised little hope for these companies to grow within, and only stood to make these huge profits for the hundreds, if not thousands of members of the unincorporated association. This meant that all legal proceedings would be carried out through all these thousands of members and was not a practical way to run. Occasionally a company could be granted a private act so that an individual could represent everyone, but these acts would only be granted to companies that were already established.
In 1844, the Joint Stock Companies Act was passed which allowed ordinary people to incorporate their business which granted new legal rights between administration and investors. Naturally this led to investors taking advantage of this, and the Limited Liability Act 1855 was passed, which limited how much investors would be liable for company losses. This meant that an investor would be liable for the unpaid portion of their shares were the business to fail. This meant investing in a corporation was much safer for investors.
Between the joint stock act and the limited liability act, the number of corporations began to grow rapidly. To match this rapid growth, business failure was on the rise as well, but investors could usually escape accountability for the business failing.
The last main development that put modern day incorporations on the track they are now was the court case of Salomon v. Salomon and Co. This court case decided that the liabilities of the owners were separate from the liabilities of the company. This meant that a creditor to a company could not sue the shareholders if the company were to fail.
There is a lot of legislation and other cases that decides how companies become incorporations, and what that means, but that is decided on a country to country basis. However, these court cases all set a path from a pre-industrial revolution system of companies to where incorporations operate in the world today.