Answer:
Plastics are polymers, meaning that they compose of essentially one molocule shape repeated continuously to for a chain of molocules with the same atomic structure.
For example a plastic shopping bag is usually made of polyethylene. The repeated molocule or monomer in this plastic is C2H4 or ethylene. Hence polyethylene.
The chemical composition of plastics is different depending on what type of plastic your dealing with.
But for the most part the raw material of plastic is hydrocarbons found naturally in oil.
Take cellulose acetate--a very popular polymer, used mostly in thin films. It's made from cotton. Some rubbers are made from the sap of a tree. The plastic in your soda bottle is made using a process that uses ethylene glycol (a major component of antifreeze) as an ingredient. Silicones are made from sand. Vinyl is made from acetylene.
petrochemicals
Today most plastics are made from petrochemicals (crude oil and natural gas), although they can also be produced from corn and other biomasses. In manufacture from petrochemicals, refineries process crude oil to produce, first, fuels, such as gasoline, diesel, and a number of different lubricants. Then they spin off a wide variety of other petrochemicals. Some of these other petrochemicals are then used by chemical plants to make a wide variety of products such as fertilizers and plastic resins. Plastic resins are, in turn, used to produce many different types of plastic.
The majority of what we know as plastic today is made from materials that are extracted from crude oil. Often the same type of crude oil that is used to produce the fuels for cars.
There are many other types of polymer, both natural and synthetic: cellulose, starch, silicones, teflon, PVC, etc.
Add And don't forget the silicones, which whilst an inorganic base, commonly contain organic materials in their composition.