Dolsot is a stone cookware, usually made with granite, that is commonly used to make dolsot bibimbop. Bibimbop, or "mixed rice," is a dish consisting of steamed rice, assortment of vegetables, and meat (which is optional). In the dolsot version, precooked ingredients are placed inside the pot and heated over the stove or open fire. The rice sizzles and turns crispy while a cracked egg cooks against the hot stone as well.
A stone pot is best for this dish but ddukbaegi is another form of cookware which can be used for bibimbop in addition to cooking various Korean stew/casserole/soup dishes. Both of these pots are very hot so it's important to protect one's hands as well as the table that it's served on.
For care, wash with lukewarm water to remove excess earthy material/dust from cookware. Wipe with damp cloth or paper towel. Repeat until fully cleaned and naturally dry. Avoid dishwasher but place water inside bowl over some period to loosen pieces of food that may stick to pot during cooking. Feel free to use dishwashing soap, rinse, wipe with cloth or paper towel and finally dry to care after usage.