Kirby & The Amazing Mirror takes place in a very large overworld consisting of nine interconnected sub-worlds (one acts as sort of a hub, but worlds often link up with other non-hub worlds). While not a persistent world in the usual sense, as it does cease functioning when the game is turned off, any area in the game can be revisited at any time ala Metroid.
Amazing Mirror has four Kirbies. In single-player mode, the player controls classic-pink Kirby, while Red, Yellow, and Green are under AI control and go about their merry ways. For the most part, everything is typical Kirby - eat enemies, take their power, use it against other enemy chumps, solve minor puzzles, beat bosses, collect key items to restore the Amazing Mirror which leads to the final boss sequence. There are several new abilities in Amazing Mirror. One of the cooler ones is Smash, which is a replica of Kirby's moves from Super Smash Bros., and since this itself is a menagerie of Kirby's copy abilities, Smash is something of a potpurri of talents.
By pressing the R button, you flip out your cellular phone (it carries three charges; batteries, like food, are a common pickup in the game world) and call in the troops. The other three Kirbies will warp in next to you and start whaling away on nearby enemies, or setting up to help solve nearby puzzles. It comes in pretty handy in boss battles, especially since sometimes they bring food and abilities with them.
In multiplayer mode, each player (up to four) brings his own GBA and Amazing Mirror cartridge. After choosing whose save file to play on, each human player takes the helm of a Kirby and the rest are AI. It operates pretty much just like the single-player game, with the exception that more than one Kirby will be doing something worthwhile. Human players could choose to travel the same path and help each other out, or they could split up and get things done many times faster. When someone phones it in, human players can choose to take the call and help out, or ignore it and carry on.
The map plays a big role in the game, as it shows room-by-room how and where the various worlds link together. It can also be used as a key for treasure items. These collectibles range from map papers (they fill out the map of a world and show how to navigate it), to sound files (which can be played with another pickup, a sound player), to spraypaint canisters (which change the color of your Kirby), to vitality powerups (which grant Kirby additional life bars).
It goes without saying that a Kirby game has minigames (or "Sub-Games"). Each of the three can be played by oneself against computer opponents, or multiplayer with a single game cartridge.
Speed Eaters: A test of patience and speed. Four Kirbies sit in front of a covered dish. Whoever eats the food first wins, but trying to eat while the dish is still covered knocks you out of the game.
Crackity Hack: A series of timing tests which, in classic Kirby fashion, see how big of a hole you can put in the planet. First some bars fill up and down (try to press A when they're full), then a target reticle appears (try to press A when it's lined up with the reticle on the ground).
Kirby Wave Ride: Each Kirby is on a warp star surfboard. You gain speed by jumping at the crest of a wave. Whoever gets to the end of the course first, wins.