What is a Bitcoin Hard Fork?

A Bitcoin Hard Fork is a software update that adds software improvements and many other changes to the Bitcoin network. When a Bitcoin hardfork happens, all clients mining bitcoin need to update the software.

If some clients continue to use the previous client, then there will be chain split of the bitcoin network and this will result in two different chains. This is why all, I mean 100% of the clients need to agree to a upgrade or there is a risk of chain splitting.

If chain split occurs, then there will be two different currencies. The chain with the highest consensus will be most likely recognized as Bitcoin and another chain will have another name.

When Ethereum hard forked after the DAO hack, there was two currencies that resulted in that hard fork. Ethereum and Ethereum Classic.