Apart from providing a legal buffer, corporations exist in business where the transaction costs exceed the fixed price costs of running a bureaucracy.
In principle there is nothing that a corporation can do which a group of individuals cannot. In practice though, a bunch of individuals will spend a lot of their resources (eg time) negotiating trade. This is the cost of trade. If they are all work for one company, their superior can just give an order (eg 'X: make a plank and give it to Y') and have it done. So in many cases it is more efficient. Corporations, though suffer from bureaucratic overhead (a form of diseconomies of scale), so sometimes a group of individuals is more efficient.
One view of communism is one very large corporation running all of society.
Corporation are also a convenient mechanism for collective bargaining.