The gates used to control the flow of water over a levee or in a reservoir is called a floodgate. Some floodgates protect areas that are vulnerable to hurricanes or typhoons.
There are many kinds of floodgates, all designed to hold water back sometimes and to let it flow at others. A figurative floodgate holds back strong emotion or something equally powerful. You'll most often find this floodgate in the phrase, "Open the floodgates." For example, a school principal might worry that allowing one student to bring his pet rabbit to class will open the floodgates for everyone bringing animals to school.