What does amuse mean?
The definition of amuse
A*muse”, v. t.
[imp. & p. p. Amused; p. pr. & vb. n. Amusing.] Etym: [F. amuser to make stay, to detain, to amuse, ad) + OF. muser. See Muse, v.]

1 To occupy or engage the attention of; to lose in deep thought; to absorb; also, to distract; to bewilder. [Obs.] Camillus set upon the Gauls when they were amused in receiving their gold. Holland. Being amused with grief, fear, and fright, he could not find the house. Fuller.
2 To entertain or occupy in a pleasant manner; to stir with pleasing or mirthful emotions; to divert. A group children amusing themselves with pushing stones from the top [of the cliff], and watching as they plunged into the lake. Gilpin.
3 To keep in extraction; to beguile; to delude. He amused his followers with idle promises. Johnson.

Synonyms
— To entertain; gratify; please; divert; beguile; deceive; occupy.
— To Amuse, Divert, Entertain. We are amused by that which occupies us lightly and pleasantly. We are entertained by that which brings our minds into agreeable contact with others, as conversation, or a book. We are diverted by that which turns off our thoughts to something of livelier interest, especially of a sportive nature, as a humorous story, or a laughable incident. Whatever amuses serves to kill time, to lull the faculties, and to banish reflection. Whatever entertains usually a wakens the understanding or gratifies the fancy. Whatever diverts is lively in its nature, and sometimes tumultuous in its effects. Crabb.

A*muse”, v. i.
To muse; to mediate. [Obs.]