Volatile liquids refer to those liquids that are easily vaporized. Vaporization is the process by which a liquid is converted into its gaseous form. During the conversion, the molecules of the liquid start to move faster, bouncing of each other at a higher rate with higher energies. This increases the pressure of the system as pressure is related to the force and frequency the molecules hit the container. Eventually, the pressure build up (vapor pressure) and the liquid will start to transform into a gas. Saying that a liquid is volatile means it has a higher vapor pressure such that it only needs to build up a lower pressure in order to be converted into the gaseous phase.
Now, this entire process is endothermic. In order for the molecules to move faster, or kinetic energy to be higher, the temperature must first be raised -- and this is caused by the system absorbing heat from the surroundings. In general, any vaporization process is endothermic -- absorbs heat.
An example of a volatile is the common hand alcohol. It feels cold when rubbed in your skin, because it absorbs heat from your body as it is being converted from the liquid phase to the gas phase.