Cats are considered smart because cats have brains that are approximately 90 percent similar to human brains. The cat's brain is also divided in two distinct areas which perform different tasks, making it possible for the cat to exchange information and develop perceptions about its environment.
These two divided areas also allow the cat to manipulate its environment. Cats also have strong memory skills and have both short-term and long-term memory. The cat's memory shapes the way that the cat learns. As a kitten, playing with other kittens in the litter teaches a cat social skills that it will remember and apply to situations as it grows older.
Cats are often thought to not be trainable, but cats are actually able to learn tasks and tricks. Cats are typically less interested in learning tricks and tasks than dogs are, but clicker training is a form of "operant conditioning" that often works when training cats.
Cat's brains are also able to experience both REM and non-REM sleep; in the REM sleep the cat will dream just like humans do. If a sleeping cat is twitching, moving its tail or making small funny sounds, then the cat is most likely dreaming.