Broken means in pieces, or no longer working. A broken plate, a broken leg, the lift is broken. It is the past participle of break doing duty as an adjective, which is where most English adjectives of this shape come from.
It stretches a long way. A broken promise was not kept. Broken English is spoken with difficulty and many gaps, and it is a set phrase that describes the speech, not the speaker. A broken home is one where the parents have separated, and a broken night is one of interrupted sleep. Note that broken and broke are not interchangeable: broke as an adjective means having no money, which is informal and unrelated.
1adjectivebrokenIn pieces, or damaged so it does not work.
“There is broken glass all over the step.”
2adjectivepromiseOf a promise or agreement, not kept.
“It was another broken promise and nobody was surprised.”
3adjectiveinterruptedInterrupted, or not continuous.
“After three broken nights she gave up and made coffee.”
4adjectivecrushedOf a person, crushed in spirit.
“He came back from it a broken man.”
Too few real examples of this word to estimate which sense is commonest.
broken is a damaged state.
Proto-Germanic
*brukanaz
Old English
brocen
Middle English
broken
English, today
broken
From Middle English broken, from Old English brocen, ġebrocen, from Proto-Germanic brukanaz, past participle of Proto-Germanic brekaną (“to break”). Cognate with Dutch gebroken (“broken”), German Low German broken (“broken”), German gebrochen (“broken”). Morphologically broke + n.
Etymology from Wiktionary, CC BY-SA