Lawn aeration is basically the punching of holes through the top couple of inches of your lawn/soil surface. The theory being it lets water and oxygen reach the roots...a good thing.
The machine they use to punch the holes is in many cases a gasoline powered rental with no noise or emission requirements...not a good thing. The tines on the machine are more than likely contaminated with weed seeds and various insect larvae that have been picked up along the way from every other house visited...a bad thing.
By allowing this machine to run over your lawn you could be playing host to a new generation of weeds and insect pests for years to come...a really bad thing.
Alternatively you could purchase a bucket of Red Wiggler worms and free them on your lawn. They aerate naturally and their castings condition the soil organically. It's also more efficient and cheaper.
This pic is from an ad I found. It read something along the lines of... Tree for sale...I'm selling it because I don't know much about trees. "Hmmm."