In addition to Phil's answer, it could also be used to invite people to enter a place or to go before you. For instance you can hold the door and say : - Hodor. or - Je vous en prie. [unsaid : allez-y, entrez !] Finally, this expression is very similar to the japanese dôzo, to invite people to do something (enter, take a seat, start a speech, anything...)

That’s a great question. Context: A: Merci. B: Je t’en prie. Pragmatically, it means the same thing as French “de rien” or English “you’re welcome” (response to “thank you”), or a bit more literally “don’t mention it.” Literally, the translation is something like “I pray thee” or “I beg you” — as in I beg you not to thank me, or I ask you not to mention it. I suppose the English “don’t mention it” is similar. Note that we use “t’ ” or “vous” as appropriate. From this point of view, it’s probably easier to say “de rien,” which, lacking a conjugated verb, is technically not even a full clause.

There is another use that comes to my mind which serves to more or less validate the action of the speaker: "Je prends plus de beurre !" "Je t'en prie ..."

Je t'en prie = De rien