Avalanche effect
One bit in should change about half the bits out — otherwise the construction is leaking structure.
The requirement that a minimal change in the input produces an apparently total scrambling of the output. For a hash function or block cipher the strict avalanche criterion, formulated by Webster and Tavares in 1985, says each output bit should flip with probability 1/2 when any single input bit is flipped.
The effect is how diffusion gets measured in practice. Without it an attacker can feed in closely related messages, compare outputs and statistically sift out key bits without breaking anything. Counting changed bits is also the first test anyone runs on a home-made hash function — shortly before realising they should not be making hash functions.