What does overdraw mean?

Answer 1

In financial terms, to overdraw is to transfer more money than a demand account contains. This is typically in the form of an "overdrawn" checking account, where the account holder has written checks whose value exceeds the account balance (for any of several reasons). This can result in checks being refused and left unpaid, and/or the payment of penalty fees by the check writer.

In Archery, it means pulling the bowstring back too far.

In communication, it can also mean to exaggerate, and thereby spoil the effect of a story or anecdote.

Answer 2

It has several meanings. In finance, it means that you take more money out of an account, than you have in that account. That means that you end up owing the bank money. Check Wiktionary for additional meanings of the word.