What does 'pas de quoi' mean in English?

The phrase 'pas de quoi' is a way of saying welcome in French, as a response to being thanked. In the Word-by-Word translation, the adverb 'pas' means 'not'. The preposition 'de' means 'from, of'. And the pronoun 'quoi' means 'what'.
Literally 'not of what' it is a contraction of 'il n'y a pas de quoi'.

Very idiomatic, it translates to 'nothing to it, not at all, don't mention it.'

Almost always said in response to an apology.