Prior learning: for this explanation you should already understand about the three different states and the differences between them.
When we heat a solid:
Heating a solid gives the particles more and more energy as the temperature increases, and they vibrate more and more. Eventually, at a temperature called melting point, the particles have enough energy to overcome the forces that are holding them in place enough to let them start to move around as well as vibrate. The solid is melting and turning into a liquid.
Heating the liquid continues to give the particles more energy, and eventually they reach a temperature, called the boiling point, at which this energy completely overcomes the forces holding them to one another. Now the particles can spread out and move freely in all directions. The liquid is boiling and turning into a gas.
Some substance turn straight from solids into gases when they are heated. Iodine is a good example of this. We call this subliming.
When we cool a gas:
As we cool a gas, the energy of the particles decreases. Eventually the energy isn’t enough to overcome the attractive forces between the particles, and they start to pack closely together, while still being able to move. This process is condensing, and the temperature at which it happens is the boiling point of the substance. That may sound confusing, but it is logical that the temperature at which a liquid changes into a gas when heated is the same as the temperature that a gas changes into a liquid when cooled.
As we continue to cool a liquid, the energy of the particles continues to decrease, and eventually this energy is too little to allow the particles to move, and the attractive forces between the particles lock them in place where they can only vibrate. This process is freezing, and the temperature at which it happens is the melting point.
Some substances turn directly from gas to solid when cooled, and this too is called subliming.
Our everyday experience tells us that liquids can turn into gases (or at least disappear somehow!) at temperatures much below their boiling points. We call this evaporation, and see it every time puddles disappear after rain. Evaporation is different to boiling.