The small plates that appear before you order anything are banchan. They are included, and they are refillable.
Banchan (반찬) arrive automatically and are not itemised on the bill. Refills are free at almost every restaurant — either ask a staff member, or take more yourself from a self-serve station if the restaurant has one. What you should not do is take them away; they are for eating at the table.
Kimchi is nearly always present. Beyond that the selection depends on the restaurant and the season: seasoned bean sprouts, spinach, braised potatoes, pickled radish, dried anchovies, seaweed, marinated tofu. A modest restaurant might serve three; an old-style hanjeongsik house can serve twenty.
Banchan are eaten alongside rice throughout the meal, not as a starter course. Take a small amount at a time with your chopsticks — they are meant to punctuate mouthfuls of rice, not to be finished first. Some are strongly salted precisely because they are meant to be eaten in small bites with plain rice.
Banchan quality is how Koreans judge an unfamiliar restaurant, especially outside cities. Jeolla province in the southwest is known nationally for serving the widest spread, and a Jeolla restaurant covering the table in side dishes is a normal expectation rather than a special occasion.