What does it really mean to "sit with" or "be present with" something?

I tend to be pretty self aware, but I realize that I don't understand really what people actually mean when they say things like "sit with" a hard emotion or "be present with" it. It seems like hollow therapy speak thats never ... Explained. Like telling people to stretch, but never specifying the muscle to stretch or how to go about it, but more vague. It seems like it means something besides just experiencing and identifying the emotion or distress, but I always either turn up woo-woo vague 'wellness' type explanations that say very little in the end of substance, or else it's sort of the same 3 line type description on official looking sites that still doesn't really ... Explain what this is or how it's done (much less why it seems to be everywhere and in everything as advice). What do you all think it means, and how it's actually done? Half the descriptions sound like something that most people get a grip on in like, middle school, but that can't be right.