Of all the various wok cooking techniques, braising is perhaps the simplest, and certainly the most relaxed and least messy. It's no wonder that it's the method employed by most home-style dishes, including the ever-popular red-braised style of cooking—in which rock sugar is caramelized in oil before adding soy sauce, a few flavorings, and a protein (pork belly works great, as do hard boiled eggs, or chunks of beef). The meat develops a deep red glossy exterior with a sweet and savory sauce that goes great with rice. I can only think of three things in the world that are better than red braised pork belly. My wife and dog barely make the list (sorry, Mom).
The term "braise" is a bit of a misnomer, as the vast majority of wok-braised dishes are not cooked for long enough for connective tissues in meat to break down, as they would in a Western-style braise or stew (though there are a few examples of this in Chinese cuisine). "Simmer" might be a more appropriate term, which is what I'll call it from now on.
Take, for example, another home-style dish: Mapo dofu (yes, it's better than pork belly). To make it, aromatics and a bit of ground beef are briefly stir-fried in oil flavored with Sichuan peppercorns, sauce and tofu are added, and the whole thing is simmered in the wok for a few minutes until the flavors have melded. If you haven't realized by now, I've got a weakness for Sichuan food.
Because the actual amount of stir-frying going on in a simmered dish is so minimal—usually limited to a small amount of ground meat and a few aromatics cooked for around 30 seconds—it's a great way for wok newbies to introduce themselves to the techniques and flavors developed in wok cooking, without having to commit to a full-on, multi-ingredient, fast-paced, ultra-high heat stir-fry. ( I admit it, that can get a little hectic your first few tries.)
The other great thing about simmered dishes is because they are essentially peasant food, the main ingredients are very inexpensive. Tofu, cheap cuts of pork, beef, or chicken, eggs, root vegetables like potatoes, taro, and cheap seasonal produce like eggplant or carrots are about as high brow as your ingredients get—a meal for four can be pulled out for easily under $10, and that's with New York prices!
Wok simmering usually occurs with the cover off, so that by the time the meat or vegetables have finished cooking through, the sauce has reduced to an intense, complex glaze that, in my opinion, is often better than the main part of the dish itself.