Note, if the engine ever quits (or really is about to) on a mag check DO NOT just run the key back. Rod Machado calls this his student's "click-click-click-click-BANG" mag check. It is not a "backfire" as mentioned earlier but an ignition of raw fuel that has been pushed out into the exhaust. Either let it die or close the throttle before moving the key again.
Here's what can happen in a mag check when switched to one mag or the other:
No RPM drop or other indication: Either the switch/p-lead is not grounding the magneto OR the engine is severely mistimed.
A small drop but the engine runs smoothly... If the drop is within the tolerances stated in the POH (typically 50-125 rpm from BOTH and within a certain tolerance to the other mag running alone)...this is normal and expected...go fly.
A larger drop or misfiring ... likely one or more the plugs has a problem: bad wriing, fouled plug, etc... If you have a multipoint engine analyzer, the affected cylinder's egt will be reading lower. Note which one it is when you take the plane back to be checked. Some will suggest some engine leaning voodoo to try to clear this, but really as a student it's probably best you get help.
The engine completely dies....mag is completely dead, or the ignition switch is faulty, or you accidentally turned it to the OFF position. Other than the last one, take it back and get it fixed.