A check that “bounces” is a check that is returned for insufficient funds. If you write a check for $100 but only have $80 in your checking account, you have insufficient funds to cover the amount the check is written for. Some banks will charge over-draft fees when this occurs.
It is possible to set up what’s called over-draft protection at your bank. When you do this, if a check is flagged for insufficient funds, the bank will withdrawal the money from your savings account to cover the difference. This service may be free if you maintain a certain minimum balance, or it may also have a fee. The fee may be worth it, so your checks aren’t returned. This is an especially valuable service if the check was for something important like rent or a car payment.