Dry ice is the solid form of carbon dioxide (or CO2). Carbon dioxide is a gas at room temperature but can be frozen to ice (dry ice) at very low temperatures a process called deposition. CO2 goes from solid state (dry ice) to gaseous state (CO2 gas) directly without passing through liquid state, a process called sublimation, the opposite of deposition. The term dry ice comes from the fact that at high temperatures dry ice will sublime into CO2 gas with out any liquid traces, unlike normal ice, which melts to form water. That makes dry ice very good for keeping things cold, because when it melts there is no liquid formation and the cooled things remain dry. When normal ice melts everything is left in a watery mess.
Did you know that dry ice is much cooler than normal ice? Water freezes at 0 degrees Celsius while carbon dioxide freezes at -78 ((minus) 78) degrees Celsius at normal pressure.