"You are welcome!"
客气=polite. So literally it means. Don't be polite (in the sense of "common we are friends, you dont need to be polite with me") 客=guest，气=breath, life force
"不客气!" can be said to friends or strangers. There isn't a separate phrase that's said to strangers, just like there isn't in English.
I think it's along the lines of "no politeness", as in, "no need to be polite"
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.
I asked a native speaker and she says it's nonsensical - "No | Guest | Gas/Temper", so it's just a phrase apparently.
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.
I haven't read enough of the vomments to know if this is in there yet but 不客气 can also be translated to, "No worries," or, "Don't worry about it." Just thought I'd put that out there because every time I come across it, I remind myself of it.