Hard forks refers to the underlying blockchain of a digital currency forks into 2 chains initially due to the underlying rules change. After a hard fork, the blockchain conforms to the revised (upgraded) rules is only considered and accepted by nodes that support the new rules, whereas the original blockchain conforms to the original rules is only recognized by nodes that support the original rules. That is, the new rules are not compatible with the old existing rules. Think of hard fork as a possible permanent divergence of a block chain that might result in splitting a chain into two, thus producing an extra new coin for every existing coin.
This is a companion discussion topic for the original entry at http://www.bitcoin-en.com/bitcoin-hard-forks-history.html