Free-feeding is when you leave a bowl of food [usually dry] out all the time for your pet to graze on when they feel snacky for your convenience. This method encourages over-eating and can cause a few issues with cats, affecting both health and behavior, especially as they age. Some cats are simply more food-motivated than others, and leaving food out for them all the time can be conducive to obesity, diabetes, osteoarthritis, and other health issues. Also, should you find yourself in the future ever trying to correct a behavioral issue, you won't be able to do it with food [most often used technique] if you always have it lying around.
Free-feeding is usually done with dry kibble, we advocate for a 90% bio-appropriate wet-food diet.
The opposite of Free-feeding is Scheduled feeding or Meal feeding. Scheduled feeding allows you to more accurately determine how much food you give your cat & makes it easier to monitor intake, give medications should you need to give them any, and provides a regular schedule for your cat which they innately crave being the creatures of habit they are. Make sure you're feeding them the appropriate amount for their age/size, and be prepared to stick to a schedule because your cat will be expecting food at the same time every day. They love the ritual and expectation that their beloved hooman will feed them at the same times every day.
Another benefit of Scheduled Feeding, is that loss of appetite for more than 24 hours is a surefire sign of a medical emergency in a cat. You can tell immediately that something is terribly wrong right away if your cat doesn't come to eat at the same time you always feed them, and react swiftly to take your cat to the ER.
In addition, free feeding goes against a cat's natural instincts, cats are not scavengers, they're hunters, and when you take that hunting out of the picture, you're damaging not only their body but their psyche as well.
Cats' bodies are built to eat small meals throughout the day. If you can accommodate it try feeding three times a day, most people do twice a day. If food is accessible to them all the time, it can disrupt their instinctual behaviors. Not to mention, overeating and indulgence isn’t good for them, and can lead to bevy of health issues. Cats need that hunting feel to satisfy their natural instincts, so get them off the free-feeding bandwagon. To quote Jackson Galaxy: "Free-feeding is the Devil"
Jackson Galaxy video on Free-Feeding
4 reasons why grazing is harming your cat | Red Dog Blue Kat
The Downside of Free-Feeding Your Cat | Hill's Pet
Why Not Free-feed Your Cat | NutriSource
Cat Feeding Myths | Dr. Jean Hofve's website
10 reasons Why Dry Food is bad for your pet | Little Big Cat
General Feline Nutrition info | the Gargoyle Catterie