How it works
A hard fork is a protocol change that splits a blockchain into two, sometimes producing new tokens for existing holders. Revenue Ruling 2019-24 holds that the fork itself is not income; income arises when new tokens are credited to an address you control and you can dispose of them. Their fair market value then is both your income and your basis.
Why it matters
Exchanges sometimes credit forked tokens months after the fork, or never support them. The income date is when you could first use the tokens, which is why two holders of the same coin can have income in different years.
Example
Your exchange credits you with 1 BCH from the 2017 Bitcoin fork in November 2017, when it is worth 600 dollars. Your income is 600 dollars in 2017, and that is your basis for any later sale.
Related: airdrop, Revenue Ruling 2019-24.