To fling is to throw something with force. You'll start a food fight in the cafeteria if you fling your vegetables at the kid across the table.
The act of throwing something recklessly or with force can also be called a fling. Your mail sorting ritual might be putting bills in one pile and personal letters in another, then giving junk mail a fling into the recycling bin. A brief period of revelry or indulgence is another kind of fling. You and your friends could plan a weekend fling in New York, staying in a hotel, eating out, and shopping without worrying about how much money you spend.