What is "Fish Sauce" typically used for?

I grew up with a Vietnamese mother that used to put fish sauce in nearly everything. While I can't exactly recommend all of her uses (she once used it in a texas beef chili -- was not good), there are a few techniques that are good to know.

A common method to create a savory sauce is to use fish sauce with sugar at a 2:1 ratio. For example, you can make Dau phu sot ca chua by sauteeing fried tofu with diced tomatoes and adding 2tbsp of fish sauce to 1tbsp of sugar. This ratio can also be used in stir-fries. I would make sure to turn on your air vents when doing this -- the smell of fish sauce hitting a hot pan is... different than what most people are used to.

It works as a savory salt alternative in a lot of dishes. I use it to season fried rice instead of using salt or soy sauce. It generally is a good idea to add this during the cooking process, so the liquid can reduce and meld with the food.

It can also be used to quick brine ground pork for savory asian dishes. I'd add somewhere in the vicinity of a tbsp per pound of ground pork. I use this technique when making Thai Krapao. There are probably other marinating/brining applications, but I don't have much personal experience with that.

You can also use fish sauce to create a wide variety of dipping sauces -- in general it is paired with something sweet (sugar or rice vinegar) to help balance out the saltiness. It is also commonly watered down (Nuoc cham) in vietnamese dipping sauces to keep it from being too overpowering.

On a personal note, my favorite use is straight up on crispy fried eggs (slightly runny yolk) over white rice. It isn't for everyone, but it's something I've been making and enjoying for years.

Fish sauce is used as a general flavor enhancer, as it is very high in glutimates, the so called umami flavor. As the Wikipedia article says:

In addition to being added to dishes during the cooking process, fish sauce is also used as a base for a dipping condiment that is prepared in many different ways by cooks in each country mentioned for fish, shrimp, pork, and chicken. In parts of southern China, it is used as an ingredient for soups and casseroles. Fish sauce, and its derivatives, impart an umami flavor to food due to their glutamate content.

Edit: I should add that it is also quite salty, so it serves to contribute to the general seasoning of dishes via its salt content as well as through the glutimate content.

And as Jefromi has kindly mentioned: fish sauce is mostly commonly used in Southeast Asia and the coastal regions of East Asia, and featured heavily in Cambodian, Philippine, Thai, and Vietnamese cuisine. BlessedGeek points out that it is also prominent in the cuisines of Indonesia, Laos, Malaysia and Singapore.

Fish sauce is liquid drained from fermented anchovies!! When I was in Vietnam we were staying near fish sauce factories, very very smelly!!

It's used to season soups (Pho for example) and sauces and dressings (as with this Lemon Grass Beef) all over Asia. It's really very strong so best only add a little at a time!

Dipping sauce for summer rolls also nice with spring rolls
6 cloves garlic (crushed)
6 birdseye chillies (finely chopped)
50ml groundnut oil for frying
25ml cider vinegar
15ml fish sauce
100g honey
100ml water
200g salted peanuts (coarse blended)

makes A LOT of dipping sauce :)

You can use it as a salt alternative in most savoury dishes. It also a imparts a distinctive "fishy" flavour pastas and most tomato based sauces. You can also use it as a budget alternative to anchovies which is getting a bit expensive.

I just used fish sauce myself for the first time, in a stirfry. The stir fry included veggies I had in the frig (green onions, summer squash, mushrooms, snow peas) along with chicken breasts (and of course garlic and peanut oil). As soon as everything was cooked, I added fish sauce (about 1 tablespoon or two) and a couple of teaspoons of Sesame oil. It was DELICIOUS! So much better than soy sauce - I was surprised. So you CAN cook Americanized Chinese food with it. I highly recommend you try it.