What it means
You're welcome. It literally means "don't be polite" — a way of saying the favor was nothing.
When to use it
The standard reply to 谢谢. 别客气 (bié kèqi) is a close variant, common in northern China.
Examples
xiè谢xie谢！——bú不kè客qi气。
Thanks! — You're welcome.
bú不kè客qi气，zhè这shì是wǒ我yīng应gāi该zuò做de的。
You're welcome, it's what I should do.
bú不kè客qi气，yǒu有xū需yào要zài再zhǎo找wǒ我。
No problem, come find me if you need anything else.
The full set of survival phrases for greetings, dining, shopping, and getting around, each with audio.