Thats your sway bar link, the verticle piece has sort of a cup on the end, and the piece where you see that screw has a ball end, where it sits nicely on the link. You can remove the link without causing any ill will to your car. People sometimes remove these links when they are hitting the trails (the more expierenced people here should be able to explain it better than me).
If I remember right, I think you need a ratchet, and a allen wrench to remove the bottom link (newbee mechanic)
They do sell a part called "quick disconnects" which allows you to easily remove the sway bar link when your going on the tough trails. I think they are around 80 bucks or so.