WHAT HAPPENS WHEN TYRES ARE UNDER-INFLATED?
Contrary to popular belief, tyres are not designed to carry the weight of your vehicle; they're designed to hold air, which in turn, carries the weight of your vehicle.
With this in mind, you'll notice a direct correlation between the maximum load capacity – printed on the side of your tyres – and the maximum air pressure the tyre can safely handle. More air pressure = More load capacity.
Naturally, the opposite is true, too.
This fact explains why under-inflation is so detrimental to a tyre because, as the air pressure drops, the vehicle's mass exceeds what the tyre can structurally handle; thus, permanent damage occurs.
However, under-inflation has several more negative effects aside from structural tyre damage.
Your vehicle's ability to corner quickly – or evasively swerve around an obstacle – depends entirely on the rigidity of your tyres, which is why racing/rally vehicles typically use low-profile tyres, or tyres with reinforced sidewalls. Stiffer sidewalls allow for sharper cornering.
Once again, the opposite is true, too. Under-inflated tyres tend to flex, roll, or wallow through hard turns, so much so that your vehicle's roll-over risk significantly increases with under-inflation.
TREADWEAR & FUEL ECONOMY
Under-inflated tyres have a larger contact area with the road; this added footprint leads to increased friction, heat build-up, accelerated tread wear, and higher fuel consumption.
HEAT BUILD UP
As mentioned above, under-inflation is a leading cause of heat build-up. Once a tyre reaches dangerous temperature levels, the risk of a "blowout" – or the total disintegration of the tyre – radically increases.
On that note, it's critically important to reduce your vehicle's speed – regardless of the terrain – if your tyres are under-inflated.
Under-inflated tyres will reduce your vehicle's steering response while negatively increasing its steering resistance.