1A reason, cause, or grounds for something; used when explaining circumstances.
遅刻したわけをちゃんと説明してください。
Please properly explain the reason you were late.
それには深い訳があるらしい。
Apparently there is a deep reason for that.
急に来られなくなった訳は仕事が入ったからだ。
The reason he suddenly couldn't come is that work came up.
2The meaning, point, or gist of what someone says; used when explaining what a statement or remark signifies.
彼が何を言いたいのか、訳がよく分からなかった。
I couldn't quite grasp what he was trying to say.
彼女の話の訳がつかめず、もう一度聞き返した。
I couldn't grasp the point of her story, so I asked her again.
子どもにも分かるように、訳をかみ砕いて説明した。
I broke down the meaning and explained it so even a child could understand.
3Rationale or justification — used to indicate that an action or remark has a legitimate reason behind it (e.g., 訳がある, "there's a reason for it").
彼のやり方には、彼なりの訳があるのだろう。
There's probably some rationale of his own behind his way of doing things.
何も言わずに帰ったのには、それなりの訳があったはずだ。
There must have been a good reason he left without saying a word.
訳もなく人を疑うのは良くない。
It's not good to suspect someone without good reason.
4The circumstances or state of affairs at the time; often used in forms like 〜という訳で or そういう訳で to explain how a situation came about.
そういう訳で、今日は会議に出られません。
That's why (under those circumstances), I can't attend today's meeting.
複雑な訳があって、今は詳しく話せない。
There are complicated circumstances, so I can't go into detail right now.
何か訳があるのだろうと、みんな気を遣った。
Everyone was considerate, sensing there must be some circumstances behind it.
5Sometimes refers to a romantic relationship or love affair between a man and a woman (colloquial, somewhat dated usage).
二人は訳があって結婚しなかったと噂されている。
There are rumors that the two did not marry because of their relationship.
あの二人の訳は周囲の人に知られている。
Those two's relationship is known among people around them.