"You are welcome!"
As someone else said, if you were to break up the sentence and translate it character by character, it would be nonsensical. That's because not all phrases can be broken down character by character to explain the translation. For some phrases, it's just the way it's said when translated to Chinese.
Actually makes sense, but you can't look at each character separately like that. 不 = No 客 = guest 气 = Air or energy. 客气 = Politeness (the "energy of guests" is to act polite) 不客气 = You're welcome (don't be polite, you don't need to thank me for this.) "You're welcome" in English has a similar origin (You are welcome to this thing you're thanking me for, you don't need to thank me for this).
Meanwhile elsewhere in the Chinese Diaspora we say "不用客气“ or "不要客气“。 That is to say "You are welcome" in response to "Thank you".
Dissected word for word "不用" or "不要" means "there's no need" or "don't". "客" means "guest" and "气" means "an air of" or "to behave like". So, the literal translation is "there's no need to behave like a guest".
I have found out that in Taiwan they say "不用谢" or "不要谢".
On the other hand, "不客气" can mean "rude" since "不" is a negation. If someone takes liberty with your personal and private things and you find out you can sternly say to the person "你不客气", meaning "you are rude (to intrude into my privacy)".
A look at how the meaning has evolved should be interesting.
The interesting thing is: you can also use ”您客气“ for the same meaning. Two phases with or without the negative word “不” share the same meaning. I know it might confuse a lot learners, but I think this is also the interesing point of the language. :-) And, “您客气” is much more 北京话 rather than mandarin.
At this point, I don't give a f*** about pronunciation. Have you listened to the average Chinese when they try to speak English or Spanish? And we can understand them with little effort, most of the times. So, I don't think I'm going to China anytime soon but anyway, let it be THEIR TURN to try to guess WTF we're trying to say!