To dine is to eat a meal, particularly the last meal of the day. When you invite friends over for dinner, you can ask them if they'd like to dine with you.
You can dine at home, or dine at a fancy restaurant — in either case, you're eating dinner. If someone tells you they "dine out on" a funny story, they mean it's endlessly entertaining and buys them a lot of good will and amusement. The verb dine comes from the Old French disner, "to dine" or "to have a meal," from desjunare, "to break one's fast."