Currently (2013-04-01) the list of Leagues is:
- Bronze League: 8% of all players
- Silver League: 20% of all players
- Gold League: 32% of all players
- Platinum League: 20% of all players
- Diamond League: 18% of all players.
- Master League: The best 2% of all players. It is impossible to qualify directly into this League.
- Grand Master: The top 200 players in a region. Is created only after 2 weeks into a new season. Players that are not active for a certain time get demoted to Master.
Before you are placed in a League, you must play 5 Placement Matches against random opponents. After that, the game tracks your skill by assigning you a matchmaking rating (MMR), which is not exactly your League points, but similar. Different Leagues correspond to different MMR ranges, and it is possible to be promoted or demoted, if your MMR stabilizes within another League's range.
After a Season ends, all Leagues are wiped, but MMR does not. To be placed in a new Season, you have to play one Placement Match, which does not actually mean more than any other match - it is just there to filter inactive players from League rankings. Skipping several Seasons does reset your MMR.
Since some patch there is also a button to Leave League - if you feel that your MMR is well in another League (like if you are constantly encountering equal opponents from there), but a promotion just doesn't come, you can try to force it. Note that this doesn't reset your MMR, of course.
There is also a special, Practice League. When you start playing on a new account, you are placed here, and can play fifty games here before your placement matches into "real" Leagues (you can leave whenever you want though). Practive League matches are played on a special, more "noob-friendly" maps, that have destructible obstacles completely blocking bases off, eliminating early pressure. After you leave Practice League, there is no way back ever.
Further reading: Starcraft Wikia
I don't know what it is by design but I can provide statistics on a per region basis. Bare in mind, this is where players are, not where they belong (so they maybe better or worse than they appear).
Region Diamond Plat Gold Silver Bronz
Global 5.48% (25,969) 16.03% (75,970) 21.58% (102,249) 21.28% (100,830) 35.62% (168,781)
North America 5.29% (10,831) 17.61% (36,060) 21.53% (44,102) 19.58% (40,109) 35.99% (73,709)
Europe 5.34% (7,604) 15.65% (22,297) 21.02% (29,944) 20.78% (29,615) 37.22% (53,028)
Korea 6.53% (3,437) 14.44% (7,599) 23.66% (12,451) 26.05% (13,709) 29.32% (15,433)
Taiwan 5.68% (1,663) 13.04% (3,820) 22.03% (6,451) 24.73% (7,241) 34.53% (10,111)
Southeast Asia 5.03% (1,170) 13.55% (3,151) 20.99% (4,882) 22.66% (5,272) 37.77% (8,786)
Russia 5.96% (952) 14.11% (2,253) 20.17% (3,222) 22.63% (3,614) 37.14% (5,932)
Latin America 5.83% (312) 14.76% (790) 22.37% (1,197) 23.73% (1,270) 33.30% (1,782)
These numbers would seem to suggest the following:
- Diamond: 95th Percentile
- Plat: 80th Percentile
- Gold: 60th Percentile
- Silver: 40-35th Percentile
- Bronze: 1st Percentile
Update:
At Blizzcon 2010 Blizzard announced that they would add two new leagues with the following requirements:
- Grand Master: Top 200 players
- Master: 98th Percentile
Best Answer
Your MMR will stay the same. It is not known what happens to MMR confidence, but it may well just not come into play, as the game will need to place you somewhere (a low confidence value does prevent you from being promoted, even when your MMR is already in another league).
So, in general the purpose is to force re-placement into a league, if you believe you're not where you belong. That is when you're tired of waiting for a promotion, or, arguably more importantly, when you are too high. Since some recent version it is impossible to be demoted mid-season, only to re-qualify to a lower league.