Many hose bibbs have a packing nut that is located behind the handle. Sometimes the packing nut will work itself loose over time and start to drip or spray water toward the handle. You can usually fix this problem by tightening the packing nut. Use your left hand to hold the hose bibb in place and tighten the packing nut with either an adjustable wrench or a pair of pliers with your right hand.

 

The silver thingy is called an atmospheric vacuum breaker and prevents water from being drawn back into the house. Every hose bibb has a vacuum breaker, but in different designs. I've had customers unscrew the vacuum breakers, thinking that they were fixing the leaking problem. The leaking is sometimes caused when the hose bibb is not opened all of the way. And it will drip water for several seconds after shutting the water off.

 

Call a licensed plumber if the vacuum breaker does start to leak.