Kinetic energy is the energy an object has because it is moving. Gravitational potential energy is the energy it has because of where it is. In the absence of friction, one converts entirely into the other.
The square is the whole story
Kinetic energy scales with the square of speed while momentum scales linearly. Double the speed of a car and you double its momentum but quadruple its kinetic energy — and since braking has to dissipate all of that energy, the stopping distance also quadruples. A car travelling at 60 km/h needs roughly four times the braking distance of one at 30 km/h, not twice.
The same square is why a 9 mm bullet weighing 8 grams at 360 m/s carries more energy than a 70 kg person walking at 1.5 m/s, despite weighing nine thousand times less.
Conversion between the two
Drop an object from height h and, ignoring air resistance, all its potential energy becomes kinetic by the time it lands. Setting mgh = ½mv² and cancelling the mass gives v = √(2gh) — which is why a feather and a hammer land together in a vacuum. The mass drops out of the equation entirely.
Where the energy actually goes
Real systems lose energy to air resistance, friction and permanent deformation. A bouncing ball returns to a lower height each time because some kinetic energy becomes heat and sound in the impact. The coefficient of restitution measures what fraction of the speed survives a collision.