It is based on the plant scientifically known as the Flagellaria indica, or more commonly referred to as the whip vine, a type of climbing plant found in tropical areas.
Whipvine is quite a decent plant given its raw stats, and thanks to its ability, it can also get you out of a tricky situation, or maybe give you an opportunity to do more damage to your opponent. For example, it can be used to move a zombie onto a lane with a tough plant like Wall-Nut for stalling, move it away to make way for a hard-hitting plant, and even force it to attack a plant to your tactical advantage (e.g. when Briar Rose is on the field and you want a zombie to hurt a flower to get rid of it).
Against
Being a pretty strong plant, Whipvine is difficult to destroy, especially since it can move one of your zombies around.
If you wish to get rid of Whipvine, you can play tricks such as Rocket Science and Locust Swarm to destroy it quickly. Cut Down to Size is an especially cheap option if you are playing as Super Brainz or Rustbolt. There are also several zombies strong enough to destroy it in one hit like Copter Commando, although most will be destroyed as well in the process if unboosted.
Gallery
Plants vs. Zombies Wiki has a gallery for Whipvine.