Final answer:
The mesosphere is the atmospheric layer where meteor showers typically occur because meteors burn up here due to increasing atmospheric density.
Step-by-step explanation:
The layer of the Earth's atmosphere where meteor showers can commonly be observed is the mesosphere. This layer starts just above the stratosphere and extends up to 85 kilometers (53 miles) high. In this region, meteors enter the atmosphere at high speeds and due to the increasing density of atmospheric gases, they heat up and burn, often resulting in a meteor shower that can be seen from the ground.
The mesosphere is situated between the stratosphere and the thermosphere, being above the layer where most weather events occur and below the region where auroras and satellites are found.