Overseeding immediately after core aeration dramatically increases the germination rate of the seed. So instead of broadcasting seed on an established turf and hoping the seed will germinate, carrying out this process after aeration will cause the seed to fall into the holes in the turf where it will have adequate seed to soil contact for germination.
Seeding after aeration is another reason to aerate in the fall. Seed has a much better chance of becoming established at this time of year and In the fall, it will germinate, mature and then become dormant - compared to seeding in the spring when the seed will germinate, mature and then will endure the heat and drought stress of the summer causing the new growth to die.