Overdraft is a special facility provided to special and valuable customers. It is a facility wherein the customer can spend more than what is in his/her account. The customer can usually spend until a higher threshold set on his/her account.
Ex: Lets say you have Rs. 25000/- on your account and the bank has given you an overdraft facility of Rs. 10000/-
Then you can spend upto Rs. 35000/- from your account.
This extra 10000 that is available to you is called overdraft.
The bank would usually charge you a fee and interest for providing this facility.