Humans have bred different dogs for different jobs and by doing so, they influenced their behavior. So called "toy breeds" retain infantile behavior in adulthood, hunting breeds have a strong chasing and hunting instinct and guard dogs are very independent and vigilant.
Caucasian Shepherd dogs have been bred to protect "their" flock of sheep against thieving humans and dangerous predators like wolves. That's where the "can be aggressive towards other animals, people and children" comes from. It was a trait that humans selectively bred into this specific breed. In the tradition of Caucasian farmers and shepherds it was common that the pups grew up with their flock and it was virtually impossible to adopt an adult dog into a new family with a different flock.
Traditionally they were also left alone with their flock for an entire night or maybe even several days. So these dogs had to protect their flock without the explicit command from their owner and be independent and autonomous. Humans bred them to think for themselves and also to be strong-headed when facing dangerous predators. In a modern lifestyle "independent" and "strong-headed" can translate to "stubborn", "ignores me" and "hard to train". If the dog sees no practical value in the command you give it, it may simply ignore your command. If the dog thinks that the vet is a dangerous predator, you'll have virtually no chance of training it to tolerate the vet.
But what does it mean that "training can be difficult"?
Most dogs can be motivated in a training either with food or toys or play. If your individual dog isn't interested in either of them, you'll have a hard time convincing it of following any of your commands. If you cannot control your dog in a civilized environment (like a town or city with strangers walking their dogs or children playing), then your life and the life of your dog will be very stressful and isolated.
If you cannot interest your dog in games, it will get bored (because it doesn't have its traditional job in our urban environment anymore). Bored dogs can get destructive and especially dangerous if the breed is known for aggressive behavior.
As a practical example: A Caucasian Shepherd dog may find purpose and pleasure in protecting you and your home. It may "protect" you from your partner or friends and it may "protect" your home from your guests. Usually you could train a dog to tolerate or ignore guests by offering it something of more valuable, like a tasty treat or some play time with the guests. But if your dog doesn't feel that those alternatives are more valuable than the "protecting" it's doing, the only alternative is to lock the dog away when you have guests. This causes a lot of stress for you and the dog, because you always have to make sure your dog cannot attack your guests (no-one accidentally opens the door to the dog) but also you have to punish your dog for doing exactly what it was bred to do (by locking it out).
How should I "prepare" myself for dealing with such a "beast"?
You can only do that by interacting with different dogs and learning about their natural behavior and body language. More specifically, you should learn from dogs with problematic behaviors until you can understand the signals they send and the motivation for their problematic behavior. There is no book or video tutorial that will prepare you enough for this particular breed. Personally, I strongly advise against this breed for first-time owners.
If the primary factor for your decision is the size of the breed, please chose a more docile one.
