There are a number of benefits. In compost, it is helping to break down materials into smaller compounds. This makes the compounds more digestable to plants and other microbes.
Good soil is full of diverse microbial activity, so this is a good sign that the process of increasing that diversity is under way.
When using the compost on plants, mycellium can make a symbiotic relationship with the plant by connecting to the roots. The mycellium can assist with moisture levels, nutrient delivery, and plant-to-plant communication.
In addition, a beneficial species of mucellium can defend the plant from other fungal species.