A hard fork (or hardfork), as it relates to blockchain technology, is a radical change to a network's protocol that makes previously invalid blocks and transactions valid, or vice-versa.
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When a Blockchain is forked, there is a permanent divergence from the previous version of that Blockchain, and nodes running previous versions will no longer be accepted by the newest version. This essentially creates two paths in the Blockchain, one path follows the new, upgraded Blockchain, and the other path continues along the old path.