What does humour mean and how is this applied to Emma by Jane Austen?

Humour (humor US) is

• (1) the quality of being amusing or laughable.


• (2) a temperament or disposition given to caprice, or unexplained impulsiveness.


• (3) to try to gratify or indulge someone eles's wishes.


• (4) an emotional, psychological state (Collins Dictionary).

(1) When applied to Emma, the first meaning of humour applies to the amusement derived from Austen's narrator's understated ironic wit along with ironic dialogue between characters, which, when understood properly, is humourously laughable and amusing.

The real evils, indeed, of Emma's situation were the power of having rather too much her own way, and a disposition to think a little too well of herself; (narrator)

(2) Jane Fairfax defines the humour associated with caprice and inexplicable impulsiveness perfectly well when she covertly describes Frank Churchill at the Box Hill outing. Her comments are not complimentary of Frank because caprice is not an admirable quality: Mrs. Churchill, who rules "with an irony hand," is said to have caprice.   

"it can be only weak, irresolute characters, (whose happiness must be always at the mercy of chance,) ..." (Jane to Frank)

(3) Mr. Knightley does not like Mrs. Elton, thinking her coarse and pushy, yet, ever the gentleman, he seeks to arrange events to her liking whenever her events have anything to do with him. In other words, he humours her by trying to gratify her wishes. She notes this herself when they are discussing arrangements for the Strawberry Party at Donwell Abbey:

"you are a thorough humourist.— ... I am fully sensible of your attention to me in the whole of this scheme ... the very thing to please me." (Mrs. Elton to Knightley)

(4) Austen's characters often speak or think of the emotional or psychological state of those around them or of their own. Emma thinks about other's being in "ill-humour," "good-humor," "the best humour," "a humour to please" or not to "please." Of Frank Churchill's psychological state, she says he is in an "odd" humour at the commencement of the ball (we learn that it is because he is being delayed from dancing with Jane Fairfax), while at the Strawberry Party, she describes him as agitated, or "out of humour":

Emma could hardly understand him; [Frank] seemed in an odd humour.

Emma listened, and looked, and soon perceived that Some people were always cross when they were hot.