Assets Under Management (AUM) is the total value of all the investments currently being managed by the fund. For Instance, let's say the corpus is Rs 18 Crores, but, due to a rise in the price of the shares it has invested in, the value of the units has increased. So the Rs 18 Crores invested is now worth Rs 21 Crores. This figure is referred to as AUM.
Check out "Mutual Funds" post in ICHP Forum. Will be very useful.