When people talk about someone being witty, they often mean that this person has a quick and clever sense of humor. They might make jokes or say things that are funny without even trying to be humorous. For example, if you're watching a comedy show and the comedian starts making light of serious topics with clever remarks, you could describe them as witty.
How common is "witty"?
Word witty is considered rare in modern English. It has a balanced usage among all categories: speech, fiction, newspapers and academic texts.
Definitions
adjective
Clever; amusingly ingenious.
Example: His speech was both witty and informative.
Full of wit.
Example: His frequent quips mark him as particularly witty.
Quick of mind; insightful; in possession of wits.
Example: She may have grown older, but she has grown no less witty.
(obsolete) Wise, having good judgement.
(archaic) Possessing a strong intellect or intellectual capacity; intelligent, skilful, ingenious.