Why did Mount Vesuvius erupt?
Mt. Vesuvius erupted due to the pressure by the magma in the Earth's mantle, which increased to the point where it had to find an outlet. The magma inside it was over pressurised and under very high temperature causing inbuilt stress that led to the eruption. The diagram below shows why a volcano erupts.
The Magma builds up over time. This then will eventually explode out of the crater. This releases an ash cloud into the atmosphere. In Pompeii this is what covered all of the people and and left a 'image' of what happened.