I don't remember how much I've talked about miso head-on, but I know it would have been before I started using it regularly. I add it to damn near anything now.
Miso is a fermented paste, which sounds off-putting, but so would cheese if I had to explain to you what it is, if it weren't a food product you were already used to and understood at a level beneath words. Most miso uses soy, making it kind of like a solid form of soy sauce -- think of it that way, as a spreadable soy sauce. Some forms of miso also involve brown rice, barley, buckwheat, millet, or other grains. All contribute different flavors, but they're all recognizably miso. The flavor is deep, rich, salty, and umami - that savory meat-like flavor of mushrooms and Marmite, aged cheese, yeast, etc.
I happen to strongly prefer barley miso, followed by brown rice miso and red miso. White miso is easier to find, but I don't think it has as pronounced a flavor relative to the level of saltiness.
Americans are mostly familiar with it through miso soup or miso salad dressings, but think of the number of different things you can use soy sauce in and you have a hint of the adaptability of miso.
Here's the main thing, though: miso is hugely useful across the board in cooking, not just in Asian or Asian-inflected dishes. It's not just a source of salt, it's an umami bomb. Sure, you can put miso on a cheeseburger, for instance -- though I still prefer Marmite or Vegemite for this -- but it goes so much further than that. You can mix some into chili. You can mix it into tomato sauce. You can mix a little with butter and rub a chicken or steak with it. You should definitely add it to onion soup. It doesn't change the essential character of any of these things -- adding miso to your pizza sauce isn't going to make anyone go "oh, that's an interesting Asian/Little Italy fusion you've got going there." It's not going to register as "Asian." It's far more broadly compatible than that.
You also don't necessarily want to build the dish around miso, because it's such a good background flavor, and you're going to overdo the salt if you include so much that miso is the strongest flavor - save that for when you use miso as a condiment, like in a dressing, glaze, dipping sauce, etc. Miso works well when you incorporate it in something that has a good foreground flavor in it - the brightness of herbs, the sharpness of onions, the spiciness of chile. Deviled eggs with miso? Probably no big whoop. Deviled eggs with miso and fennel? Probably awesome.
My standard Buffalo wings sauce now uses miso, for instance -- melt a little butter, whisk miso into it until it's thickened, add a vinegar-based hot sauce (Louisiana, Frank's, Texas Pete, or homemade pepper mash):