1Counter for occurrences (times) — attached to numbers to count how many times something happens, e.g., 一回 (once), 二回 (twice), 三回 (three times). One of the most basic counters in Japanese.
この映画はもう三回見た。
I've already watched this movie three times.
一回だけチャンスをください。
Please give me just one chance.
週に何回ぐらいジムに行きますか？
About how many times a week do you go to the gym?
薬は一日三回飲んでください。
Please take the medicine three times a day.
彼は何回も同じ間違いをした。
He made the same mistake over and over.
2A time; an instance — used as a noun to refer to one particular occasion, as in その回 (that time) or この回 (this time/occasion).
彼に会ったのはその一回だけだ。
I only met him that one time.
この回の会議は特に重要です。
This time's meeting is especially important.
前回の話の続きですが——。
To continue from last time's conversation —
3Inning (baseball); round; period of play — used as a unit to divide the progress of a game, especially in baseball.
試合は五回裏に逆転された。
The game was turned around in the bottom of the fifth inning.
三回の表にホームランが出た。
A home run was hit in the top of the third inning.
九回まで投げ切ったピッチャーは見事だった。
The pitcher who threw all the way to the ninth inning was magnificent.
4Episode; chapter; installment — a colloquial noun/suffix usage for one segment of a TV show, serialized story, or streaming series, as in 今週の回 (this week's episode) or 最終回 (final episode).
この回のテーマは友情だった。
The theme of this episode was friendship.
先週の回を見逃したから、今夜配信で見るつもりだ。
I missed last week's episode, so I'm going to catch it on streaming tonight.
最終回はとても感動的だった。
The final episode was really moving.
5An abbreviation for the Hui people (回族), a Muslim ethnic group in China. Effectively never used standalone in modern Japanese; appears only as part of the compound 回族.
6An abbreviation for 回教, an older Japanese term for Islam. Modern Japanese uses イスラム教 instead; the bare 回 in this meaning is essentially never seen in contemporary writing.