1The area behind a person or thing; the rear. Used in expressions like 後を追う (to chase after) or 後をつける (to tail someone).
犬が飼い主の後をついて歩いている。
The dog is walking along behind its owner.
刑事は容疑者の後をつけた。
The detective tailed the suspect.
はぐれないよう、私の後について来てください。
Follow behind me so you don't get separated.
2After; later — the time following an event or point. This is the most common everyday sense. The formal written equivalent is のち, and the bound Sino-Japanese suffix is 〜ご (as in 卒業後).
会議の後で、みんなでランチに行った。
After the meeting, we all went to lunch.
宿題をした後で、テレビを見た。
After doing my homework, I watched TV.
詳しいことは後で説明します。
I'll explain the details later.
3The remainder; the rest. Used as 「後は〜だけだ」 to mean what is left to do or remains.
宿題は終わった。後は遊ぶだけだ。
I've finished my homework. All that's left is to play.
準備はほぼできた。後は当日を待つだけだ。
The preparations are almost done. All that's left is to wait for the day.
ケーキは半分食べた。後は冷蔵庫に入れておこう。
We ate half the cake. Let's put the rest in the fridge.
4An adverbial use meaning how much remains — 「あと五分」 (five more minutes), 「あと二つ」 (two more). Placed before a quantity or time.
試験まであと五分だ。落ち着いていこう。
Five minutes left until the exam. Let's stay calm.
あと二つ集めれば景品がもらえる。
If I collect two more, I can get the prize.
ゴールまであと少しだ、がんばれ。
Just a little more to the goal — hang in there!
5In casual speech, placed at the start of a phrase to mean 「also」 or 「and another thing」 — a colloquial connector for adding an item to a list.
卵と牛乳、あとパンも買ってきて。
Get eggs and milk, and also some bread.
参加するのは田中さんと佐藤さん、あと私です。
The ones taking part are Tanaka, Sato, and also me.
6One who comes after — a successor, heir, or descendant. Common in the phrase 後を継ぐ (to succeed to / carry on).
社長の後を息子が継いだ。
The president's son succeeded him.
この店の後を継ぐ者がいなくて困っている。
We're troubled that there's no one to take over this shop.
7After someone's death; used in the phrase 亡き後 to refer to the time following a person's passing.
祖父の亡き後、家業は叔父が守った。
After my grandfather passed away, my uncle kept the family business going.
8(Archaic) an old-fashioned sense meaning the past or a previous time. Essentially no longer used with this meaning in modern Japanese.