What is an economic system and what is its function?

All we people constitute the economic system. Each of us participate in the making of something (some work directly in factories- like car factory, some in services like transport). Then we are paid money for our participation (in the form of salary). We then buy the things we need. This cycle of making things, buying and consuming them constitute the economic system.

In the middle of all this, there are people like doctors and actors, who do not 'make' anything, but who provide 'services' (healthcare and entertainment). Their 'salary' is what others pay them. Salary is nothing but a 'token' which society gives a 'member' for his contribution to production, so that he can buy things.

If each can make all we need - e.g. if each can make his own car, food, TV, phone, etc. , then there may not be an economic system. It cannot happen. Individual groups are engaged in making different things (car, TV, etc). Each member gets paid salary in a common way (dollar, rupee, etc) which he uses to buy things.

The above system BROADLY constitutes an economic system.

In rawest terms it keeps people from slaughtering each other for food and other items.