Why do volcanoes and earthquakes occur at destructive plate margins?

Destructive plate margins are where a plate of higher density is subducted, or forced underneath, another, less dense plate.

This occurs due to convection currents in the mantle.

These are caused by radioactive decay which produces heat, causing the hotter, less dense material to rise and then sink when it cools down again (like the heating of a room by a radiator).

Volcanoes

Melting of the mantle occurs above the subducted plate.

The magms (melt) is less dense, so it rises up towards the crust.

The magma pushes through the crust, and erupts at the earth's surface as a volcano.

This can be very explosive (example, Mount St Helens eruption, May 1980).

Earthquakes

As the plate is being subducted, it can sometimes become stuck on the overriding plate.

The subducting plate is still trying to force its way down into the mantle, so there is a build up of force.

This can also drag the overriding plate down with it (a good way to visualise this is to use your hands as the plates and see what happens when one gets 'stuck').

If enough force builds up, this causes the plates to jolt suddenly past each other, with the overriding plate pinging back up.

This releases energy, which is felt as an earthquake.