A puppy mill is a place where dogs and cats are kept in isolation inside very small cages without any attention or affection. They are bred over and over again to produce as many offspring as possible, and they are typically underfed and mistreated. Once a dog or cat has ceased being able to produce offspring, it may be killed or abandoned. By buying pets from a pet store, you will be perpetuating this market. People also typically impulse buy from pet stores because the animals are cute and displayed in a shopping environment.
Pets bought impulsively often end up in shelters.
The problem with this is that this is also an impulse buy, and the animals again end up in shelters. The movie 101 Dalmatians spurred a huge demand for Dalmatian puppies, many of which ended up in shelters. Shelter workers predict that there will be a huge influx of Chihuahuas because of Taco Bell's latest advertising campaign. A second issue that is important is that dogs and cats are not people. Behaviors displayed-chewing on furniture, defecating on the floor, etc. are not vindictive actions.