Welcome to Hairball Season!
A cat's tongue is like a comb, and they use that comb constantly. Imagine if you combed your hair dozens of times a day. Now imagine the hair that would collect on that comb. You - being a human - would pull the hair off and toss it in the trash. But for a cat, that's its tongue, and it has no choice but to swallow all those loose hairs.
The hairs tend to collect in the cat's stomach, forming a wad. The cat's stomach is designed to retain the hairs, rather than passing them through the intestinal tract. Presto: hairball.
When a hairball gets too big, it can interfere with a cat's digestion. This is why you may see your cat vomiting up undigested food after a meal. If the cat eats too much food, there isn't room for it, what with that big hairball taking up all that space.
The cat will try to relieve its discomfort by eating thread, twigs, grass, and other roughage. These can either "sweep" the hairball through the stomach into the intestinal tract, or they can encourage the cat to throw it up. Either way is a win, from the cat's perspective.
As your cat's caretaker, you have the same basic options. If you have an indoor-only cat, it will greatly enjoy a little tub of grass. You can buy grass seed and sprouted grass at the pet store. Or you can visit a supermarket and scout out the produce department for tubs of wheat grass. This is the exact same grass, but at about a third of the cost!
You will want to be prepared with a roll of paper towels, of course. I have become quite deft with sheets of newspaper, and my cats have become accustomed to me rushing over and sliding a sheet of paper before them when they start hurking. (You know - hurking. "Hurk! Hurk! Hurk!")
In the other direction, "Hairball Control" cat food is typically cat food with extra fiber. That fiber helps scrub the hairball down into the intestines. Another great option is to give your cats a bit of canned pumpkin with every meal.
NOTE: You will want to buy 100% canned pumpkin and NOT canned pumpkin pie mix.
Surprisingly, most cats love canned pumpkin, and will eat it without any further coaxing. Feed about a tablespoon once a day.
And finally, this classic is still a gold standard of hairball care: the plastic tube of hairball paste. This is basically just fish-flavored petroleum jelly. It's inexpensive, and it works quite well. Most cats will eat it right off the tube. For more reluctant cats, you can sneak up and smush it onto their legs, thus forcing them to lick it off. (Be sure to put it on their upper leg. If you put it on their paw, they will often just flick it off. And that stuff makes a real mess on the carpet!)
Photo credit: Flickr/Mat Booth