the arrow indicates the direction of flow, if you put it on the wrong way the water could push the jumper closed, depending on the type of stopcock...
a stopcock is pretty much like a regular tap in construction, water goes in through one end, passes through the valve, and out the other end, but it doesnt go straight through like it would in a gate valve for example, it goes through in an S shape, in-up(through the jumper seating)-turn-out, if it was fitted the wrong way it would go in-turn-past the "tap washer"(pushing it onto the seating) and no further. Most stopcocks have jumpers that are attached via a thread to the handle so that it will hold the jumper up(open) whether the water is pushing against it or not, it still causes extra stress on the stopcock though.
Imagine the outlet on this pic comes from the side and not the bottom...
IN--->
--->OUT
btk