Minecraft has two aspects to it: One is that it is a fantastic building game that challenges players not just to create, but to gather materials to do so from the surrounding environment (example: to build a ladder, one must chop down trees, craft the wood blocks into wood planks, then the planks into sticks, and then finally build the sticks into a ladder). Crafting is carried out on a Crafting Table players create fairly early on in the game, and consists of arranging items into an approximate picture of what you want on a 3x3 grid. Players must also smelt ore acquired from mining in a furnace, and cook meat and fish and craft Bread in order to keep from starving to death.
The second aspect can be slightly eerier: In any mode other then Peaceful, various monsters will spawn at night. They would be frightening in appearance if not for their blocky, 8-bit appearance. This doesn't keep them from looking slightly unsettling, however. Zombies will lurch at players with their arms spread in front of them, and Skeletons will fire arrows from the dark. Endermen look the most disturbing of them all. Based on the Slender Man of urban legend, they stand a block taller then the player, are pitch black and very thin, and having glowing purple eyes. When the player breaks eye contact with them, they will become enraged (their mouth will open and they will teleport around the player, striking them from behind). They come nowhere close to the Creeper, however. Lizard-like in appearance, they have four legs, no arms, a ghost-like frowning face, and a mottled green skin tone. These are Minecraft's mascot mob for a reason. Looming out of the dark, this creature will sneak up behind a player, or march unrelentingly after them. When they reach a certain range, they will explode, dealing vast amounts of damage to the player, often resulting in a "game over" screen. The fact that the cave-bound Creepers will most likely target a player carrying a mother load of Diamond and Emerald (The two rarest minerals in the game, as they are nearly impossible to find) gives them the ability to startle even the most seasoned Minecrafters.
Players can also visit a flaming, lava-filled, monster-infested wasteland (based on a, um, place that shall remain nameless) called the Nether, and a floating island filled with Endermen and ruled by a fierce dragon (the games primary boss) called the End. So yes, Peaceful mode is advised, but Caverns (the daytime home of Mobs who venture out/naturally spawn at night) are still dangerous, with lava and water lakes, perilous, massive falls to adjoining caves far below. If you buy the Xbox version, it will come with a Tutorial level, but if not, look up the guides on the Minecraft Wiki linked on the site. It'll be a life-saver.
In conclusion, if you can avoid the monsters and caves, it'll be great for most kids. But if you have a child who can handle the dangers, Survival mode is one of the most enjoyable sandboxes I've played in.