Turbulence is the rough air that airplanes fly through that cause it to shake. It can range from mild to severe. Mild turbulence will make the drink in your cup slosh around but severe turbulence will make everything spill out.
Most turbulence can be predicted. Some weather conditions such as summer afternoon thunderstorms can cause turbulence. Other times it is reported by airplanes flying through it. Clear air turbulence is most dangerous because it can come out of nowhere.
Aircraft are designed to withstand the stress of prolonged exposure to severe turbulence. The biggest danger is being thrown against another object such as the ceiling or a wall during severe turbulence.
The most important thing to keep yourself safe is to obey the seat belt sign. Any time the sign is on keep your seat belt buckled low and tight across your lap. During moderate to severe turbulence the flight attendants will be buckled up in their seats and you should be too.