Extended warranty and damage protection plans are two separate things.
An extended warranty covers the computer and its components (usually not the battery though) for a specified period of time. It warranties them against defects in manufacturing, malfunction, or failure due to everyday use. It does not include anything you do to the laptop (although sometimes its hard for them to prove that you messed it up).
A damage protection plan is usually sold above a warranty (i.e. you need to get the warranty and then pay extra for this). The damage protection plan covers, typically, any accidental damage done to the laptop for the specified period of time you purchase it for. Accidental damage is stuff like; spilling liquid on your laptop, dropping it, etc. Some of these plans even include protection against theft (though, not many, and they will always specify if they do).
If you are accident prone or clumsy, a damage protection plan may be in order.