Factory warranty is basically a contract with the manufacturer. Under this contract, the manufacturer absorbs either the repair or replacements cost for a pre-defined period of time.  It benefits the customer by exempting them from spending over the purchased price during the contract duration.
 
How does one extend the factory warranty?

Different factory warranty plans are available [...]

New Car Warranty:  What Is It?

A new car warranty or “Bumper-to-Bumper” warranty covers all breakdowns except parts specially itemized in the policy. Once you get a new car warranty coverage plan, you will get service for failure or breakdown of most parts, other than the listed items for exemption. It’s the most integrated coverage available. [...]