Aerating is important for your lawn to be full and thick, and is most effective in the fall, but can also be done in the spring, when moisture is present. Aerating during dry periods can cause the soil to dry out. Pulling cores is the most effective form of aeration.
Pulling cores creates a hole that will, in turn, be filled by the soil around it causing a loosening up overall. Compacted soil hinders turf growth, and eventually will cause it to decline, just as we see between soccer goals and on football field centers where traffic is more intense. Athletic fields must be decompacted many times more than an average lawn, and may be sliced or aeravated during game times to avoid cores on the playing surface.
Pulling cores also has other benefits. A thatch layer should be about 1/2 an inch thick; too thick will impede movement of fert and insecticides into soil, promote increased disease and insect issues along with reduced heat, cold, and drought hardiness and shallow rooting. Core pulling, which places cores of soil on top, causes the thatch layer to decompose. Not only does this maintain the thatch layer, but the clippings, which still contain the nutrients added to the turf as fert, along with other organic materials, decompose into humus, thus enriching soil. Putting clippings back down, rather than bagging, equates to needing less fert applied to the lawn. Holes also allow water and air down into the turf. The consistent routines of fertilizing, mowing, and core pulling form a cycle that produces quality turf over time by improving soil conditions that the turf grows in.
Your local turf contractor can pull many cores utilizing a machine such as the Zspray Zplug. Top notch tractor mounted reciprocating aerators are made by Toro. The more cores pulled the better. Initially it does not look good, but it will do wonders as time passes.