YesBalala wrote:

My laundary faucets has a valve at the back which got a small plastic
pipe leading into the drainage pine in the basement. Recently,
whenever I turn on the water tap of the faucet, water coming out
normally (from the tap) as well as from that small pipe. Any idea why
and how can I fix it?

It is called a "trap primer". The hose is supposed to feed a
small amount of water to the drain in order to keep the trap filled
with water.

More info he
http://www.plumbingwarehouse.com/trapsealprimers.html

Or
GOOGLE
for: "trap primer"

Jim