When someone is snappish, they are impatient and speak in an annoyed way.
Snappishness is not very nice because it means someone is being grumpy or rude.
Examples:
Her snappishness made everyone quiet.
I don't like his snappishness.
The dog's snappishness scared the cat.
His snappishness is like a grumpy bear.
The teacher's snappishness made the students afraid.
The snappishness in the air was like a storm.