Why do air bubbles rise to surface of water? I was asked this question by my son and I want to give him the correct answer. So keep it simple please.
Here is what he asked. Why do air bubbles rise when they are released underwater? 
 A: You can start off by citing a common example: a helium filled balloon goes up. You should ask him why does it go up when everything else is being pulled down? The answer is that the density of the balloon is far less than the density of the air.
The same goes for a bubble in water. The bubble contains air which is less dense than water; therefore, the bubble rises.

Why do less dense objects rise inside water?
The water molecules are in continuous motion and they often bump into the bubble. When they bump into the bubble, they push the bubble. The water molecules bump into the bubble from all sides: up, down, left, right, forward, back. Due to gravity, the pressure at the bottom of bubble is higher than the pressure at the top of the bubble or in other words, the force exerted by the water molecules which collide at the bottom of the bubble is more than the force exerted by the water molecules at the top of the bubble. Gravity does not exist sideways; therefore, the forces applied from the right, left, forward and backward cancel out. You are left with a net upward force due to the water. Your bubble has some weight, however, the weight of the bubble is not significant enough to cancel the upward force applied by the water. Therefore, the bubble rises.
Mathematical Derivation:
Consider water in a container in equilibrium.

Take a tiny block of water of height $h$. This block of water has weight but why doesn't it compress the water below and fall down? It is because the water below applies a force larger than the force applied by the water above such that the net force on the block of water is zero. 
$$upward force = downward force$$
$$(P + \Delta P)A = PA + mg \tag{1}$$
The mass of the water in the block can be expressed in terms of its density.
$$m = \rho V = \rho Ah \tag{2}$$
Substituting $(2)$ in $(1)$, we get:
$$(P + \Delta P)A = PA + \rho Ahg$$
$$P + \Delta P = P + \rho hg$$
$$\Delta P =\rho hg$$
The pressure below the block is $\Delta P$ more than the pressure at the top of it.

$$F_{net} = \Delta P A - mg$$
$$F = V\rho g - (V\sigma) g$$
$$F = Vg(\rho - \sigma)$$
The net upward force depends on the difference of the density of the fluid and the body immersed. As the bubble is less dense, there will be a net upward force.
A: The bubble rises to the surface because it weighs less than water. If there's a bubble of air in a water bottle, the water is being pulled down by gravity and the air is being pulled down by gravity – and water pushes the air out of the way. 
There are some funny tricks because of this fact. The water pushes the air out of the way, but the air has to have somewhere to go. For instance, when you take a clear bottle of soda and turn it upside down, and it looks like the soda is floating on air. The soda is definitely heavier than the air (or really carbon dioxide in soda's case) but the soda is pushing down on the gas evenly. 
Yashas Samaga in the above answer thoroughly described density. The reason he did so was because how many molecules you have a in a volume, say in a bottle, matters. Each molecule has weight. For instance, water is $\mathrm{H_2O}$ and air is a mixture of approximately 78% nitrogen, 21% oxygen and 1% argon with some other gases. The water molecule is less massive than the air molecule, so it actually weighs less than an air molecule! But, if you have a bottle of water and a bottle of air and the bottles are the same size, there are many many more water molecules in the water bottle compared to the number of air molecules in the air bottle. The density of water makes it weigh more than the air. That's why we talk about the density.  
If you get air very very cold, just like how if you get steam cold, it turns to liquid water, very cold air will turn to liquid air (which is more dense than water and if you could stably mix liquid water and liquid air and somehow prevent the liquid water from freezing, the liquid air would sink to the bottom).
A nice follow up question would be asking why ice floats on water. It's not the only solid that floats in its liquid form, solid silicon and arsenic behave in the same way. The reason that ice floats on water is because the ice crystallizes. In water, the $\mathrm{H_2O}$ molecules float very freely over one another. In solid form, they lock in place. Normally with solids, the molecules lock tightly next to each other. In the case of ice, the molecules lock in place rather far from one another which makes ice less dense than water. 
A: The answer you seek depends on the age of your son.  

You could use Archimedes principle which states the upward force on a body in a fluid is equal to the weight of the fluid displaced by the body.
So the two parameters are the weight of the body and the weight of the fluid it displaces.  
If the weight of the body (rock) is greater than the weight of the fluid it displaces (air) there is a net downward force on the body and it falls.
If the weight of the body (air bubble) is less than the weight of the fluid it displaces (water) there is a net upward force on the body and it rises.
You can in turn categorise the three conditions in terms of densities and state that an object with a higher (average) density than the density of the fluid will sink, an object with a lower (average) density than the density of the fluid will rise.  
If the weight of the body (ship) is equal to the weight of the fluid it displaces (water) there is a no net force on the body and it floats.

If you son is happy with falling objects in air then you can tell your son that what he is seeing is water falling in air.
The falling of an object in air can be thought of the potential energy (energy of a body due to its position) of the air and the object as being reduced.  
When the object goes down the air it displaces goes up.
The object falling loses more potential energy that the air which it displaces gains in rising.  
A: Density of air is much less than density of water so upthrust will be more than the weight of air bubble inside water so it rises up.
A: Gravity plays the ciritical role. In a "zero-gravity" or gravity free environment, the air bulb has to always stay at the location it produced.
A: Air bubbles rise to the surface of liquid. The reason being that owing to excess of pressure inside an air bubble (Pi-Po=2T/R) they are less dense  and get pushed towards surface.
A: When the bubble is formed at the lower surface of water,it exerts excess pressure. due to which the pressure increases at the bottom than the surface.And the upthrust makes the bubble to rise up. As it rise up,the pressure decreases and the size of bubble get larger.
