Tires can explode from overheating, general wear and tear, being made to carry too much load, or being put under too much stress.
So if Airplane tires have to carry very heavy loads, can be retreaded up to 7 times and undergo at least 500 landings before each retread, and experience extreme stress and heat during every landing...
Why don´t Airplane tires explode?

On the outside, an airplane tire may look a lot like any other tire, but in fact, they are completely different

Composition.
In order to withstand the extreme stresses they have to, an airplane tires are made by combining layers of different materials, these materials are synthetic rubber compounds, aluminium reinforcements, nylon fabrics, steel reinforcements, and aramid fabrics.
Aramid fabrics are strong, heat-resistant fabrics used in ballistic-rated body armor and other military and aerospace applications.

Conductive Rubber.
The synthetic rubber used for airplane tires is called conductive rubber, meaning that it can actually conduct electricity.
On a modern aircraft, there are hundreds of electrical components and sensors that are very sensitive to electrical discharge.
During takeoff and landing, the friction of an Airplane's tires creates static electricity, should this energy suddenly discharge it could interfere with or damage these sensors and have catastrophic consequences.
The conductive rubber allows the tires to conduct that electricity into the ground and therefore avoid a potential build-up of static and its subsequent discharge.

Nitrogen.
Aircraft tires have to be inflated to 14 bar in order to carry the burden of the massive aircraft above them, they also have to endure extreme pressure changes and drastic temperature changes. During a normal flight, a tire's temperature can go from -40ºc to over 200ºc in a relativity short period of time.
Normal pressurized air is affected by temperature change, it's corrosive, and, it's flammable.
So in order to reduce the level of expansion and contraction that the tire suffers during these changes, reduce internal corrosion, and lower the risk of an explosion or fire, airplane tires are actually filled with the inert gas, Nitrogen.

Safety Measures
Airplane tires are also equipped with some pretty ingenious safety devices.
As we mentioned before, aircraft tires have to endure extreme pressures and heat, even though they are filled to 14 bar, the tire itself has to be able to withstand 4 times that pressure for at least 3 seconds in order to be deemed "Safe".
In addition to this, most aircraft wheels are equipped with an OPRV, Over Pressure Relief Valve to release the tire's pressure should it exceed a safe level.
Another safety device wheels have is a Thermal Fusible plug.
This plug has a central core made from a metal that has a low melting point, normally lead or tin.
Should the wheel or tire exceed this temperature during a heavy braking situation, the inner core melts, slowly releasing the tire's pressure and therefore reducing the possibility of an explosion and improving braking by increasing the friction the tire has with the ground.

Circumferential Grooves
Airplane tires don't have the intricate tread patterns that car tires do, just some circumferential grooves, oddly enough, this is also done to stop them from exploding.
A tire's tread is designed to evacuate water from the surface beneath it to increase traction and avoid aquaplaning.

The horizontal tread that we see on a car tires design doesn't appear on an airplane tire because the average aircraft's tire hits the runway at 150 mph and it must accelerate to that speed as it is dragged along the runway,
this stress would literally rip the block-like car tire tread from the tire and possibly cause it to explode.
Also, aircraft really have no need for the horizontal tread anyway.
The horizontal tread is designed to evacuate water as we go around a bend giving us traction when we corner at speed. Should you ever be in an airplane that's cornering at speed, aquaplaning, probably isn't your biggest worry!

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