1A school class (e.g., "1st year, class 2"); when attached as a suffix after a grade it can be pronounced ぐみ.
うちの子は今年3年2組になった。
My child is now in 3rd year, class 2.
2組は教室で発表の準備をしている。
Class 2 is preparing their presentation in the classroom.
2A group of people; a party, team, or crew. Also used as a counter for pairs/groups of people, as in 二人一組 ("in twos").
彼はいつも三人組で学校に来る。
He always comes to school with a group of three.
捜査は二人一組で行われた。
The investigation was carried out in teams of two.
彼女たちは幼なじみで、いつも同じ組で行動している。
They're childhood friends and always act as the same group.
3A lot, bunch, or set — a grouped collection of items of the same kind.
皿を一組揃えて新居に持って行った。
I took a set of plates to my new home.
楽器は三組に分けて運ぶことになった。
The instruments were divided into three lots for transport.
4A crime family; an organized-crime syndicate (e.g., a yakuza group).
その事件は組同士の抗争が原因とみられる。
That incident is believed to have been caused by a feud between crime syndicates.
警察は暴力団の主要な組を摘発した。
The police cracked down on a major crime syndicate.
5A set or assortment of items (e.g., a deck of cards); also used as a counter for matched sets.
トランプを1組買ってきてください。
Please buy a deck of playing cards.
来客用に布団を一組用意した。
I prepared a set of bedding for guests.
6In printing, typesetting or composition — the arranging of type and layout (a technical term).
この本は組が読みやすくて評判がいい。
This book's typesetting is easy to read and well regarded.