A check isn't only a mark that's made when an assignment has been handed in or a task completed—it's also a piece of paper that represents money. A personal check works like cash. As you know, you give it to someone to whom you owe money. That person can turn your check into cash or use it just like money. A check is like a promise to the person you're giving it to that the amount you've written on the check is backed up by money in a checking account.
A checking account is a type of bank account. Checking accounts aren't investment accounts because you generally don't earn any interest on the money you keep in the account. Depending on the type of checking account, you may have to keep a certain amount of money there (called your balance). The balance generally is figured on a monthly basis and is called a minimum monthly balance. That balance on average during the month can't dip below a set amount (such as $100 or $1,000). If it does, you'll be charged a fee.
A check is proof that you've paid for something. A check is readily accepted as payment by most places and should be used instead of cash when sending payment by mail.