1To differ (from); to be different — used when two things are not the same in nature, content, or state.
あなたの意見は私の考えと違う。
Your opinion is different from mine.
国によって習慣が違う。
Customs differ from country to country.
写真と実物では色が違って見えることがある。
Sometimes the color looks different in a photo than in real life.
同じ料理でも店によって味が違う。
Even the same dish can taste different depending on the restaurant.
2To be wrong; to be incorrect — used when an answer, statement, or fact is mistaken.
答えが違うよ。もう一度考えてみて。
That answer is wrong. Try thinking about it again.
それは事実と違う。
That's not true.
日付が違っているので直しておいてください。
The date is wrong, so please correct it.
3To become mentally deranged or abnormal — almost always used in the fixed phrase 気が違う ("to go out of one's mind"). Rarely used on its own outside that idiom.
あまりの恐怖に、一瞬気が違ったのかと思った。
The terror was so intense that for a moment I thought I was losing my mind.
4Kansai dialect sentence-ending usage, roughly "isn't it?" / "wasn't it?" — often as ～のと違うか, similar in meaning to standard ～じゃないか.
今日、雨やったんと違うか。
Wasn't it raining today?
それ、あの店の新メニューと違うか。
Isn't that the new menu item from that restaurant?