Fungus

[McClain's]

What is the brown round ball shape fungus and when stepped on it lets out a puff of brown smoke? What causes it and how can it be gone?

[Damian]

Is that a fungus or mold?

[SWD]

Post a picture. It sounds like a mold.
High humidity/rain and not enough air movement/sunlight are two contributing factors. Compaction in the soil causes a build up of toxic levels of CO2 in the soil which creates limited gaseous exchange in the soil which helps to promote the mold.
Raise your mowing height, aerify and check the soil fertility level in the soil. Once the turf is cared for better, on C4 turf the mold should abate without spraying.

[topsites]

What is the brown round ball shape fungus and when stepped on it lets out a puff of brown smoke? What causes it and how can it be gone?

a fart spore lol

I know what you're talking about, it lets out brown smoke when you hit it with the mower or weed-eater as well, don't know what it's called thou... Careful, that smoke is dust and contains spores and I wouldn't be for breathing that stuff.

It's a type of a mold, that's the closest I can think of.

[Grassmechanic]

What is the brown round ball shape fungus and when stepped on it lets out a puff of brown smoke? What causes it and how can it be gone?
A Puffball.

[TurfProSTL]

We get some that look like cow patties.

I always thought they were the fruiting bodies (like mushrooms) of a soil fungus. Forget the name of it, if I ever knew it.

Aerate. Trim/prune to improve circulation and light infiltration. Good luck.