In the case of morels, it's thought a forest fire does two things. Firstly, it damages or kills the trees the fungus obtains food from while growing underground, which is thought to signal mushroom production. Secondly, it helps to clear out the plant litter (leaves, twigs, etc.) covering the forest floor, giving the mushrooms an easier path to the surface. The cup fungus Geopyxis carbonaria tends to show up in the same fire-damaged forests as morels. It appears earlier, so it might be a useful guide for where morels (one of the major products of North American forests - hundreds of tonnes are harvested each year) can be found.
Here are a couple of cool photos I found on Flickr:
|Morels growing in a burned out stump hole (Source)|
|Cup fungus growing where a campfire once burned (Source)|
|Peziza pseudoviolacea growing at a recently burned site (Source)|
|Rhizina undulata growing on a tree root in a recently burned forest (Source)|
Greene DF, Hesketh M, Pounden E. 2010. Emergence of morel (Morchella) and pixie cup (Geopyxis carbonaria) ascocarps in response to the intensity of forest floor combustion during a wildfire. Mycologia 102(4):766-773. [Full text]