What are Plastic Bags made from?

Plastic film is made from polyethylene. Polyethylene is a very simple molecule, a carbon chain forms the "backbone" and each carbon atom has two hydrogen atoms bonded to it.

The picture above shows a chain of 8 carbon atoms forming a polyethylene molecule. In reality polyethylene molecules have carbon backbones that are many thousands of atoms long.
High density polyethylene is comprised simply of long polyethylene molecules. Low density polyethylene has branches from the carbon backbone. These branches improve the toughness and tear-resistance, but reduce the tensile strength.

How is Plastic Made?

Plastics are made from hydrocarbons, as the name implies hydrocarbons are a category of molecules that are made from hydrogen and carbon. Hydrocarbons can be small molecules such as ethane (see picture below) or large molecules with carbon "back bones" or carbon rings. Hydrocarbons are naturally occurring in oil and gas deposits.

In Australia plastic is made from Natural Gas. Natural gas is mainly Methane (one carbon atom), with some ethane (two carbon atoms), a little less propane (three...) and butane (four...) etc.
The natural gas is "cracked" into ethylene by heating it to high temperatures.

Ethylene is converted into long polyethylene molecules by heating it in the presence of a catalyst. The polyethylene is pelletised and bagged.