Mood or temper; a polite/respectful way to refer to someone's state of mind or spirits.
先生に会ったら『ご機嫌いかがですか』と挨拶した。
When I met the teacher I greeted him, 'How are you?' (polite).
あの人は最近ご機嫌がいいようだ。
That person seems to be in a good mood lately.
ご機嫌を損ねないように注意したほうがいい。
You should be careful not to offend/put them in a bad mood.
Well‑being; a polite way to refer to someone's health or overall condition/safety.
お年寄りのご機嫌を伺いに訪ねた。
I visited to check on the elderly person's well‑being.
長旅の後、皆のご機嫌を確認した。
After the long trip, I checked on everyone's condition/well‑being.
先生のご機嫌を損ねると授業が早く終わるかもしれない。
If you put the teacher in a bad mood, class might end early.
Used adjectivally to mean being in a good mood; cheerful or in high spirits.
今日はよく眠れたのでご機嫌だ。
I slept well today, so I'm in a good mood.
彼女はプレゼントをもらってご機嫌になった。
She became cheerful after receiving the gift.
ご機嫌で歌を口ずさんでいる。
Humming a tune in high spirits.