It's a polite and formal way to respond to someone who has thanked you for something. It's similar to saying "It's my pleasure" or "No problem" in English.
Here's a breakdown of the phrase:
* どうぞ (dōzo): This means "please" or "here you go."
* いたしまして (itashimashite): This is a polite and formal way of saying "I did it" or "I have done it."
Together, the phrase conveys the sentiment of "Please do not mention it, I was happy to do it for you."