The AKC inspects breeders and anyone who makes registration transactions (25 a year or more). So, if you own or co-own a bitch that has had a litter that is registered with the AKC, it is possible to be inspected. The generally accepted rule is that the AKC will inspect breeders who have 7 litters in one year (the breeder gets put on a list to be inspected). But, inspections can also come in response to complaints .
The inspection is basically a check to see that a breeder is in compliance with AKC rules - including paper work, care of the dogs, identification of the dogs, and proper registration. Basically, they inspect your records, the conditions where you keep the dogs, and sometimes they do DNA tests on puppies to verify documented parentage.
Here is a good website with some first-hand informaiton from someone who was inspected.
How to Survive an AKC Inspection