When a solid is heated, the heat energy goes to the particles. It makes them vibrate more and more, and eventually the strong forces between the particles, that hold them in the rigid lattice, are overcome, and the particles start to move around. The solid has now melted.

When the liquid is heated, the heat energy goes to the particles, which makes them move faster. There will be some particles, which will move faster than others. The fast moving particles at the surface of the liquid will overcome the forces of attraction from other particles and escape. This is known as evaporation.

When the liquid gets hot enough, almost all the particles have enough speed and energy to overcome the forces of attraction and escape each other. At this point big bubbles of gas form inside the liquid as the particles break away from each other. This is known as boiling.