In English, oftentimes verbs don't make complete sense unless, as in your example, they have an adverb part that goes along with them. Sometimes the adverb is literal, meaning it tells you exactly what it means; sometimes it is figurative, meaning you have to memorize the actual idea of the verb-adverb construction. The verb "to throw" means to propel something (by hand) through the air from one place to another. You can throw a ball, and your dog will chase it. In your example, "throw off" indicates that the clothes are being thrown, and the direction is down from the balcony. So the couple in your example probably had a very big fight, and the woman got so mad that she threw his clothes off the balcony. If you just said, "She threw his clothes," I would picture her lifting his clothes maybe off the bed or off the floor and just tossing them across the room. Other examples: She threw a penny off the Eiffel Tower. The baby threw her bottle off the table. The gangsters threw the informant off the bridge. There are other figurative meanings of "throw off" that you would have to memorize because the "off" does not mean "down and away." Examples: I was thrown off by her answer. ("Thrown off" means "confused by" or "surprised by.") He threw off his clothes and jumped into the lake. ("Threw off" means "took off quickly and carelessly.") She threw off all inhibition and posed nude for the artist. ("Threw off" means "freed herself from.") The convict threw the dogs off his scent by walking into the river. ("Threw off" means "lost" or "distracted.")

"To Throw" is a verb that means to toss, to cast away, to cause to fall, to propell through the air. Past tense is "threw". I threw a ball in the air and caught it. I threw the towel on the table. I will throw my trash in the waste-basket. I threw some things together and put them in my suitcase then went on a trip. I threw my dirty clothes in the basket and will wash them tomorrow. The girl threw his clothes off the balcony and let them drop to the ground below.

It means "put clothes hastily off"