Evaporation is the process of a substance turning from its liquid form to its gaseous form. This occurs when a substance (in liquid form) is heated to a certain temperature - this temperature varies between substances and is called the boiling point. What happens is that as heat is applied to the liquid the particles inside it absorb the energy from the heat and become more and more excited (they vibrate more quickly) as more heat is applied. Eventually the particles become so excited that they break free from the surface of the liquid and become vapour. Evaporation has occurred at this point.
The reason a liquid becomes a gas when the particles become excited is that a gas has much weaker inter-molecular bonds than a liquid. A solid has the strongest inter-molecular bonds so that is the most difficult state of substance to manipulate.