what is core aerfying of a lawn? How to do it?

It's also known as aeration, and a lawn company will bring a machine to run over your lawn that takes out little segments of the soil to let more air down to the roots if your lawn is overly "thatched". That means it has a ton of dead stuff down by the roots preventing air, water and nutrients from penetrating the sod very well. The machine leaves little "cores" of sod laying on top of the grass so it looks like a whole pack of dogs were out there . . .

In some places with nice, loose soil it's really not necessary, but if you have heavy clay soil and you don't collect your grass clippings, but let them mulch, it's not a bad idea to do it every few years.

Depending upon where you are, this isn't necessarily the greatest time of year to have this done. Springtime is better when the grass will grow back quickly. Would you fill in your profile with your location, please? This will help us to answer your questions better in future.

The core aerator tool can be rented at places like Home Depot. Here is a video...at first I thought the man was running too fast but then I realized that this machine is self-propelled.
https://www.youtube.com/watch?...

There are manual core aerators but (in my opinion) they require way too much effort. If you have a riding lawn mower or tractor, there are pull behind models that can be purchased or rented.

Hey Pager,
If there is a rental place near you they should have them, though you might need help loading and unloading it ( they are HEAVY and in my opinion the heavier the better. ) while I agree that your location dictates when you should do this, nearly any landscape pro or web site will tell you spring AND fall are the opportune windows for ( core ) aeration and in the summer, if you fell the need, use dagger ( straight blades without the hollow core ), this prevents your soil from drying out. If you decide to aerate or have someone do it, remember the more passes you make or different directions you do it from, the better. If it looks like the tenth annual cats#*t competition was held in your yard, then you did it right!

When you core cultivate, you're also leveling your grass area and filling in low spots, so don't rake up the 'mess' left behind.

I would also suggest that you put down some grass seed immediately after. Just be careful where you get your seed, if you read the back of the package, most will have anywhere between 2-12% weed seeds. That doesn't seem like much until you realize that for every 100 seeds you use 2- 12 will be weeds!

Finally my last bit of advice (thank goodness, huh?), Don't fertilize until the grass has been cut twice, this will keep fertilizer burn to a minimum.