Tyre Pressure Monitoring Systems (TPMS) are a way of warning a driver that a tyre is incorrectly inflated, which will decrease the safety and performance of the vehicle, and increase the risk of an accident.
It is difficult to spot an under inflated tyre visually, especially without a fully inflated tyre as comparison. Due to the rigidity of current tyre walls, a drop in pressure will only lead to slight increased flexing of the wall when the tyre is viewed at rest. This is why TPMS can be advantageous, it can warn drivers that their vehicle has an under inflated tyre despite the tyre looking normal.
There are many dangers to having under inflated tyres, because they are designed for use at their recommended pressure. Under inflation can lead to increased deformation in the tyre wall as it concentrates the load upon the tread shoulders, this reduces the amount of surface contact the tyre has with the road. This can have many consequences.