1. What is DAO?
Distributed Autonomous Organization. A collection of smart contracts which govern an organization through voting by it’s token holders. DAO was also the name of the project by Slock.it which got hacked.
2. What function had the vulnerability?
3. Why was the hard fork initiated?
Initially they attempted a soft fork, but discovered it would introduce additional security flaws so it was abandoned. At this point the decision to hard fork was put to the community who decided the damage was too severe to ignore. The vote to hard fork passed. Once the hard fork completed the portion of the community who disagreed continued mining the old branch and Ethereum Classic was the result.