Cold water faucet not working

My cold water faucet in my kitchen is not working properly. This is the problem. The cold water valve is open, cold water comes out fine. But for some reason, I am unable to turn it off with the faucet knob on top. Even if the knob is turned completely off I can open up the cold water valve and water will pump out. So my question is, is there something that needs to be "adjusted"?

A picture would help or a brand name. Probably needs a repair part, but hard to tell what from your scant description.

The age of the faucet and brand name would be very helpful.