Boiling:
The temperature of a liquid increase on heating and vapour starts rising from the surface. When the liquid reaches a particular temperature, it gets vigorously agitated and the whole volume of the liquid starts to transform into vapour. This state of the liquid is called boiling.
The temperature at which the whole volume of a liquid starts transforming into its vapour state rapidly under a fixed pressure is called the boiling point of that liquid at that pressure.
Evaporation:
The gradual change of a liquid to its vapour state at any temperature from the surface of the liquid is called evaporation.