the cryptocurrency world a fork is when a there is a change in the rules of the blockchain that the coin operates on or the nodes disagree on a historic transaction(s).
Think of a hundreds of people walking down a road and the road comes to a fork, some people may decide that they do not want to follow the traditional direction of the masses and take the other route – as they believe it to be better. This would split the crowd and others may follow. In terms of cryptocurrency the minority of followers would create a new coin (think of Bitcoin Gold, Bitcoin Cash).
Soft forks are quite common, in the rare cases when two or more miners validate a block at the same time they will each product their own hash (verification code) for that block. This often gets resolved as the next block is added to the blockchain and then the nodes can verify that this chain is the longest and most valid chain, rendering the other chain invalid.
Hard forks are intentional and are imposed by the developers of a blockchain. The developers impose a hard fork to change the rules of the blockchain. Bitcoin is on an open source blockchain, therefore developers can impose changes at any time. There are 2 ways a hard fork can go:
1. The majority of nodes do not agree with the new rules and continue as normal. If the fork occurred and a percentage of nodes did follow the new rules, the majority would reject their blocks and force them to create their own coin(take Bitcoin Gold for example).
2. The majority of nodes agree with the change in rules and the nodes that run the existing rules are forced to either change rules or they fork off and create a new cryptocurrency