Lawn aeration reduces soil compaction and the accumulation of thatch, thereby increasing water and fertilizer uptake in soils which invigorates grasses and stimulates new growth.  Aeration is especially important in lawns growing in heavy clay soils and in areas with heavy pedestrian or vehicular traffic.  
    The accumulation of water on the surface of a lawn is sign that aeration is indicated.   You can also remove a section of lawn and see how far deep the roots reach.  If the roots only go down an inch or two, it may be that aeration would be important.  See: 
content (vt.edu
Here is some additional information on lawn aeration:
Lawn Aeration | University of Maryland Extension (umd.edu)