The cap turns a change in level into a pulse.
Suppose the left side of the cap is high and the right side is low. The capacitor is charged.
If the left side suddenly goes low the cap is still charged so the other side of the cap MUST go to a negitave voltage of the same size ( but different sign ) as the origional voltage across the cap to preserve the energy in the cap.
The cap can now discharge and this negitave voltage is removed. Thus a high to low transition on one side produces a negitave pulse on the other.
The reverse happens when the low on the input changes to a high, a positive pulse is produced on the other side.