The difference between these two points lies in their names itself, that is, melting means to melt and boiling means to boil.

Basically, melting point is the temperature at which a substance melts, that is, changes from solid state to liquid state whereas boiling point is the temperature at which a substance changes its state from liquid to gaseous state.

By taking an example of water let’s make this a little easier-

Ice is the solid form of water, at 0 degree centigrade or lesser than that but it melts to water at or above 0degree. This water, when heated upto 100degree or more turns into vapour, i.e., it starts to boil. Thus melting point of water (rather ice) is 0 degree centigrade whereas its boiling point is 100 degree centigrade. These can vary with the presence of impurities.

I hope this helps.