How is a mushroom a decomposer?

Let me try to put this delicately. Mushrooms feed on poop and other decomposing things. Thus recycling the poop.

Awesome! Mushrooms (and bacteria) are the only life forms that can break lignin which protects the cellulose in plant cell walls.
A practical use of mushrooms is to decompose tree stumps and clean oils spills. If you really want to get to know mushrooms watch this.

Yes, but they can be scary, as this article shows:

“THE LARGEST living organism ever found has been discovered in an ancient American forest.

The Armillaria ostoyae, popularly known as the honey mushroom, started from a single spore too small to see without a microscope. It has been spreading its black shoestring filaments, called rhizomorphs, through the forest for an estimated 2,400 years, killing trees as it grows. It now covers 2,200 acres (880 hectares) of the Malheur National Forest, in eastern Oregon.

The outline of the giant fungus stretches 3.5 miles (5.6 kilometres) across, and it extends an average of three feet (one metre) into the ground. It covers an area as big as 1,665 football fields.”

ROOOAAAARRR PANDO (trees roar right?)

I recommend the book “Mr Bloomfield’s Orchard” by Nicholas Money. It’s a very informative book about mushrooms and other fungi and still manages to be entertaining.

We have a mushroom farm within a half a mile of our house. They used to compost there, and it was interesting when the wind blew the right way. When an ex-farmboy friend first smelled it, his comment was “chicken poop, (although he used a more colorful word) yup, chicken poop. You actually get used to it after a while, and it starts to smell good.