Banchan means small dishes of food that served along with rice in Korean restaurant. Most of them are vegetable-based like cucumber, radish, and pickles.
Banchan was considered as a result of buddhist influence near the mid-three kingdom period. At around 57AD to 668AD, Buddhism was the predominant religion in the country, and buddhists all against eating meat because of their religion.
Only after the Mongol invasion, people can again add meat into their diet but they still keeping the banchan as part of the Korean food culture. Time after time, Koreans added more varieties of banchan like fish cake and samsaek jeon but most of them are still vegetable-based. Even though many people misunderstand that banchan have only kimchi, in fact, there are less than half banchan are kimchi.
Kimchi: you can eat it raw with steam rice or make a fried rice with it.
Rice paper: wrap the meat and vegetable with rice paper. Some Korean restaurants give out free lettuce wrap or rice cake pieces for wrapping and some restaurants serve free rice paper for the same purpose.
Radish paper: serving with same purpose like rice paper and it goes really well with Korean pork belly.
You can always ask for free refill on banchan in any Korean restaurant. I personally love the fishcake and spicy fermented cucumber the most;.