A fork in crypto is a change to a blockchain's protocol that splits the network into two possible paths. Every blockchain runs on agreed-upon rules. When those rules change, the nodes on the network either accept the new rules or stick with the old ones. Depending on the type of change and how much of the network adopts it, the result is either a seamless upgrade or a permanent split into two separate chains.
Think of a fork like a highway diverging: both roads start from the same point, but they lead to entirely different destinations.
The most important distinction in blockchain forks is whether the change is backward-compatible. A soft fork introduces new rules that are stricter than the old ones. Nodes running the old software still recognize new blocks as valid, even if they cannot produce them. A hard fork introduces rules that are incompatible with the old software. Nodes that do not upgrade cannot validate new blocks and effectively fall off the main chain.
Soft forks are less disruptive because they do not require universal adoption. Bitcoin's Segregated Witness upgrade in 2017 was a soft fork: it changed how transaction data was structured, but old nodes could still participate in the network without upgrading.
When a hard fork occurs and the network does not reach consensus on which chain to follow, you get two live blockchains. Both share a common history up to the block where the split happened. After that point, they produce separate blocks independently.
If you held coins before the split, you typically have coins on both chains afterward. Bitcoin Cash split from Bitcoin in August 2017. Anyone who held Bitcoin at the time of the split received an equivalent amount of Bitcoin Cash, because both chains recognized the same transaction history up to block 478,558.
Many forks result from governance disagreements within a developer or miner community about which direction the protocol should take. The Bitcoin and Bitcoin Cash split was triggered by a disagreement over block size. Bitcoin kept a 1 megabyte block limit to preserve decentralization. A faction favoring larger blocks to increase transaction throughput forked the chain.
Ethereum's fork in 2016 following the DAO hack is another major example. The Ethereum Foundation voted to reverse transactions that drained $60 million from the DAO smart contract, which required a hard fork. A minority refused to accept the reversal and continued the unaltered chain as Ethereum Classic.
Sources:
https://ethereum.org/en/history/
https://bitcoin.org/en/faq
https://www.sec.gov/offices/oe/fintech.htm