Extended warranty insurance extends the manufacturer's original warranty by a certain amount of time which is usually one year. This gives you extra time in the case that the item you purchased breaks, malfunctions, or quits working. Warranties will usually cover the cost of parts and labor to repair your purchased items.
In order to be eligible, you'll want to pay for the item(s) using the credit card that is offering the extended warranty. You'll want to check what items are and aren't covered with the extended warranty insurance.