1To 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.
彼女は本に視線を落とした。
She cast her gaze down at the book.
2To 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.
3To 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.
4To 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.
5To 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.
警察は厳しい尋問で容疑者を落とし、自白させた。
Through harsh interrogation, the police broke the suspect down and got a confession.
6In 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.
7In martial arts (esp. judo), to render an opponent unconscious with a submission hold such as a chokehold.
彼は絞め技で相手を落とした。
He rendered his opponent unconscious with a chokehold.
8To 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.
9To end a period of fasting or dietary abstinence (somewhat archaic/literary; the origin of the term 精進落とし, the meal that ends a mourning period).
四十九日の法要が終わり、ようやく精進を落とすことができた。
After the 49th-day memorial service ended, he was finally able to end his period of dietary abstinence.
10Colloquial: 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.