A Shiny Pokémon is an alternately colored variant of a Pokémon. They can be caught in any Pokémon RPG from Gold and Silver onwards, though the probability of catching or finding one is 1 in 8192. The one major exception to this rule is the shiny Red Gyarados present in the Lake of Rage in all versions of the Pokémon Gold, Silver, and Crystal games. The term "shiny Pokémon" is not officially acknowledged in English media (although it seems to be a widely-used slang term in Japan; Ken Sugimori uses it in the title of a piece of artwork featuring a shiny Charizard), but "Alt. Color" (rUD, irochigai?) does appear among the options the player can choose filling out forms in the third generation of games.
Since first-generation games do not recognize shiny Pokémon, there is no distinction unless the Pokémon is traded to a later version.
Shiny Pokémon are not necessarily better than regular Pokémon, but in the metal generation games, they have a 10 (in 0-15 range) gene in Defense, Speed and Special. The Attack gene is either 2, 3, 6, 7, 10, 11, 14, or 15. ([8/16]*[1/16]^3 = 1/8192 probability.) In the GBA generation, however, "shininess" is not determined by the genes, but by another value and are effectively the same as any other Pokémon in battle. Most shiny Pokémon are considered to be collectors' items in the games since they are so rare.
In the Ruby, Sapphire and Emerald versions you can still catch a shiny Pokémon with the same odds (there are also shiny Pokémon in the FireRed and LeafGreen Versions). However, shiny Pokémon do not have different stats from normal Pokémon. Shiny Zigzagoon were given out from GameStop and EB Games in July 2004. Also, in FireRed and LeafGreen, some Pokémon have been preset to appear as their alternate color counterparts in the Trainer Tower. However, since they are under the control of your opponent, they are non-obtainable.
The term "shiny" is not explicitly stated in the metal generation games, and it is in fact a term invented by the Pokémon fan community due to the flash of stars appearing as the Pokémon enters a battle, unintentionally implying a sheen or crystalline property to the colors of the Pokémon. This minor animation was originally intended so that one could identify a Pokémon was shiny even if playing Gold and Silver on a monochrome Game Boy.
In the advanced generation of Pokémon games, there are several methods of getting Shiny Pokémon other than the dismal chance normally presented. The most obvious one is to catch the Red Gyarados that appears in the Lake of Rage.
Another, more complex trick involves trading the Red Gyarados to a Red or Blue version, teaching it the Mimic TM, and trading it back. Then, using the move deleter in Blackthorn City, the player deletes all the moves except Mimic. Then, the Gyarados is traded back to the Red or Blue version and battles a Ditto. Battling the Ditto, the Gyarados uses Mimic after Ditto uses Transform. Gyarados can then use Transform. It then transforms into Ditto, after which Ditto transforms into the transformed Gyarados. After that, the player catches the Ditto, which will be shiny when traded to Gold, Silver, or Crystal.
Another, even more complex trick involves restarting the game; it does not always work, so it is dangerous to do. The player takes the name ??w?x?y (case sensitive), then uses a combination of the Missingno. trick and the aforementioned Shiny Ditto trick. Before doing this, the player must look at a Pokédex entry for Ditto. Once this is done, the Shiny Ditto trick can be used on a level 230 Missingno., which will only know Transform. The Missingno. must be level 230 for this to work. When the Missingno. is caught, it will have the DVs of a shiny pokemon. When traded to a Gold or Silver version, if the game allows it (sometimes it may say the Missigno. is unusual and cannot be traded) it will be a Shiny Pokémon. If the "ghost" form of Missingno. is traded properly, it becomes a Shiny Lugia.
These were excerpts taken from Wikipedia.org.
A Shiny Lugia doesn't sound so bad, does it?