服气 is a very common term in everyday, informal conversation. Its connotation can range from sincere admiration to sarcastic exasperation.
Acknowledging Superior Skill: This is the most common usage. It's said after a competition, watching a masterful performance, or seeing someone solve a difficult problem with ease. It's a sign of respect.
Ending an Argument: When someone presents an irrefutable point or evidence, you can say “我服气了” (wǒ fúqì le) to mean “Okay, you've convinced me, I give up.”
Sarcastic Exasperation (服了你): The phrase “我服了你” (wǒ fú le nǐ) is a hugely common variation. It literally means “I submit to you,” but it's almost always used to mean “You're unbelievable,” “I'm speechless,” or “I give up on you.” It expresses exasperation at someone's foolishness, stubbornness, or bizarre behavior.
The Negative Form (不服气): The opposite, 不服气 (bù fúqì), is just as important. It means “unconvinced,” “defiant,” or “unwilling to concede.” It shows a fighting spirit and is often used by someone who has lost but doesn't believe the outcome was fair or that the opponent was truly better.