The trees leaves make a kind of cover that cover over the other plants in the rain forest.

What is this part of the rainforest called?

canopy.

http://rainforests.mongabay.com/0404.htm

The part of the rainforest you are referring to is called the canopy. The canopy is the uppermost layer of the forest formed by the dense, overlapping branches and leaves of the tallest trees. It is often referred to as the "roof" of the rainforest as it creates a continuous, leafy cover that shades the lower layers of the forest. The canopy plays a crucial role in regulating the environment of the rainforest by intercepting sunlight and reducing the amount of rainfall reaching the forest floor. It provides habitat for a wide variety of animal species and is a key component of the rainforest ecosystem.