To cause something to fall (drop). More broadly used for losing something, casting light or one's gaze, pouring in liquid, or leaving something behind.
通りで財布を落としてしまった。
I dropped my wallet on the street.
テーブルからコップを落として割ってしまった。
I knocked the glass off the table and broke it.
舞台にライトを落として、中心を照らした。
They directed a spotlight onto the stage.
To remove (dirt, makeup, paint, etc.). Colloquially it can also mean to spend money at a place, to omit/remove an item, or to leak/let information escape.
寝る前にメイクをしっかり落とす。
I thoroughly remove my makeup before going to bed.
あの店で散々お金を落としたよ。
I spent a lot of money at that shop.
重要な項目を会議の議題から落としてしまった。
An important item was left out of the meeting agenda.
To lose (a match), to reject an applicant, to fail (a course/exam), or to be defeated in an election — also used transitively as 'to fail/reject someone'.
彼は大事な試合で相手に点を取られて試合を落とした。
He conceded points to the opponent and lost the important match.
面接で候補者を一人落とした。
We rejected one candidate at the interview.
彼女はその科目を落として再履修することになった。
She failed that subject and has to retake it.
To lower or reduce something (amount, voice, production, weight), to worsen quality or reputation, or to speak ill of / belittle someone.
彼は声を落として小さな声で話した。
He lowered his voice and spoke quietly.
ダイエットして体重を落した。
I lost weight through dieting.
不祥事で会社の評判を落としてしまった。
The scandal damaged the company's reputation.
To capture or take (an enemy stronghold), to force surrender or secure acceptance; also used in stronger/older senses like bringing someone into wrongdoing or making something one's own.
王国は三日でその城を落とした。
The kingdom captured the castle in three days.
交渉で相手の主張を落として、条件を飲ませた。
In negotiations they overruled the other's position and forced them to accept the terms.
In computing, to download or copy data from a system to another medium.
そのファイルを自分のパソコンに落としておいてください。
Please download that file to your computer.
In martial arts (esp. judo), to throw or bring an opponent down (to make them fall/unconscious in some usages).
彼は見事な投げで相手を落とした。
He threw his opponent down with a brilliant throw.
To deliver the punch line or the concluding twist of a story/joke.
彼は話の最後にうまく落としたので、会場は大笑いした。
He landed the punch line well at the end of his story, and the audience laughed.
To finish a period of fasting or similar religious/ascetic practice (somewhat archaic/literary).
三日間の断食を落として、徐々に食事を再開した。
He finished the three-day fast and gradually resumed eating.
Colloquial: to win someone over, seduce, or conquer someone's unwillingness (e.g., 'to pick someone up' or 'to seduce').
彼は見事に彼女を落とした。
He successfully won her over.
あの営業は客を落とすのが上手だ。
That salesperson is good at winning over customers.