Why do earthquakes often happen near subduction zones?

That is where the movement occurs!

A subduction zone is where one tectonic plate is sliding under another one. It is not usually a continuous smooth motion, but an intermittent cycle of building pressure of one plate against the other and then a "slip" or movement that relieves the pressure by moving the plates.

This movement is an earthquake. The impact of the pressure/motion waves through the earth actually are felt across the entire planet. But only the areas close to the actual movement feel a distinct - sometimes catastrophic - shock.

Thus, the areas near a subduction zone will feel the effects of this movement as an earthquake more frequently and severely than other parts of the world.