Banchan is your typical set of a bijillion side dishes that unload the table during each meal. They can be a lot of things, but the staples tend to be kimchi, a spicy cucumber thing, cold potatoes with a sweet cream, japchae (sweet potato noodles, personal favorite) and often some cold blanched beans sprouts. There are many more, all of which are tasty, delicious, and varying in textures and taste.
Spicy fermented cabbage really wasn't a winning name, so we keep to calling it kimchi here in the United States. And it really is so much more delicious then its unglamorous description. Spicy, crunchy, and like wine, full of varying flavors that make each and every jar a bit different, it's the must-have at every Korean meal, whether as a side or incorporated into the main dish in some delicious way. Koreans are known to fly back to the United States with cases of this stuff. The most authentic kimchi is a long and complicated process, but there are also several recipes for quick kimchi you can make at home as well.
Every culture has a great meat dish to prey on, and for Koreans bulgogi (sometimes called Galbi, difference is in how thick or thin it is sliced) is the basic signature they like to stand on. Beef, chicken, or pork can be used (almost always beef though), but the key being the special marinade of soy, sesame oil, sugar, garlic, pepper, and other magical things, grilled over open flame that make it so magical. The fanciest serving is often over a burner right at your own table, ensuring the fresh and hottest bites you can get, often making for a fragrant meal. Bulgogi often goes into various dishes as well, particularly their big rice dish, bibimbap.
One of the most comforting Korean things you can have after a long hard day, bibimbap basically means "mixed rice." It comes in two ways, the basic way where a rice is topped by a variety of vegetables, usually kimchi, shredded carrots and various greens along with a fried egg on top, or the spectacular and often worthy of the extra dollar or so dolsot bibimbap, which puts the rice in a hot stone bowl which caramelizes and crisps the rice to perfection. Both bowls usually come with a bottle of magical red pepper paste sauce, which gives the dish a deep sweet and spicy flavor. It's really pretty when it hits the table, but the secret to eating it is to get everything together and mash the hell out of it until you get something like a fried rice consistency, and then enjoy.
No really! Usually vegetables thinly sliced with chunks of seafood depending on the type of panjeon, or just vegetarian, it's a thin savory pancake often served as an appetizer. I sometimes wake up in the morning and fry up a batch for breakfast for a hearty breakfast.
Think of it as the Korean version of gnocchi, these chewy pieces of dough are made from rice cakes, pan-fried lightly and then tossed in a spicy sauce for a warm and comforting bite. Really addicting with the chewy rice cakes and sauce.
There's plenty more to explore as far as Korean food is concerned, but this guide hopefully acts as a decent head start into the world of Korean cooking. It's really tasty stuff that's fairly healthy and just flat out good. Do yourself a favor and head out to a local restaurant to get a big, giant bowl of bibimbap with all the fixings now!