Roots need oxygen!
Many people don't know this important fact because they are always told that trees take in carbon dioxide and release oxygen through photosynthesis. However this only occurs in the canopy, and much of the oxygen created there is used by the leaves and stems.
Soil compaction, which is very common in urban environments, can significantly reduce the pore space needed for oxygen to reach the roots, which is where aeration comes in very handy. Aeration can also be a major help when it comes to fertilizing.
If a tree is in an area that also has turf grass then simply spreading fertilizer on the surface will have a minimal impact on the tree. This is due to the fact that the grass will absorb most of the nutrients before they reach the tree roots. The holes created during the aeration help the compost and fertilizer bypass the grass roots, significantly increasing the amount of nutrients absorbed by the tree roots.