Well shinies are a interesting thing. They are special Pokemon with different colors that you have a very small chance of encountering. Your chances are 1 in 8192. That seems like a lot but here are some tips on how to encounter one of these rare specimens.
Tips for Encountering Shinies
There are a couple things you can do to make your chances of encountering a shiny better.
The first thing is the PokeRadar and here is how to do it: use repels to avoid any unnecissary Pokemon. Then use PokeRadar to encounter a pokemon. You are trying to get a chain of Pokemon, the higher the chain the higher the chances you have of encountering a shiny. I would suggest a chain of around 40-45 as your best bet.
There is another way however it is brutally boring. You can spend days and days running around your pokemon's area trying to get a shiny.
The last way is for Set Pokemon such as Darkrai, Dialga, Palkia, Ect. You have to stand by them then save. Battle them and if they aren't a shiny, soft reset by pressing Start+Select+L+R. Then keep battling until you get a shiny.
Are shinies stronger than normal Pokemon?
No they are not. In the Metal Generation, aka G/S/C, they were, but now, shinies have the same abilites, moves and stats that normal Pokemon do. Nowadays, shinies are only good for trading around WiFi for better Pokemon.