A resident permit is a document proving that you're effectively residing in China (contrary to L, F, other visa type) and it's often link with a particular type of Visa (Z, L-family gathering,...).

According to your status, you can have a "resident permit" or a "permanent resident permit".

A person holding a resident permit can :
- travel in and out of China as many times s/he wants within a year,
- buy one appartment

Also, depending the country you come from, if you hold a resident permit here, you may not have to pay taxes in your country, but only in China as you're no more considered a "resident" of your home country.

To get a resident permit :
- having a fixed employment contract
- since 2010, if you're married with a Chinese citizen, you can get a resident permit (one year for adult, two years for children).
- invest a lot of money
- open up a business

I put a link to the Gonganbu with all kind of information about visa and resident permits (in English and in Chinese).

- since 2010, if you're married with a Chinese citizen, you can get a resident permit (one year for adult, two years for children).

Actually, this may not be the whole story. I have been married to my wife since 2009. I came here a few months ago to live here for an extended period of time. We went to the PSB to apply for the Residence Permit in Nanning, but instead of the Residence Permit, they issued me a 6 month visa. Their reason was that it was the first time I had applied for a Residence Permit so they decided to give me a 6 month visa first and then after that I can apply for the Residence Permit. So, just because the Chinese government says you can APPLY for the Residence Permit, that does not necessarily mean that you will GET it. It is at the discretion of the local PSB office where you apply for it.

A residence permit is issued by the local PSB in your community, and it takes over (replaces) your visa, by removing time limitations.  It is issued under special conditions to those that qualify for it, and it works as a visa even if called a permit. 

For example, if you have an "L" type visa, to get one you must be married to a Chinese Lady / Men to qualify for one.  Normally, the first time you get one for 6 months stay, and comes with single entry (cheaper) or multiple entries (more expensive).  On your next round, you may get one issued for one year if still married.  If divorced, you may be refused.  After five years, you can get one good for two years, the so called "senior residence permit", which cost twice of a normal one.  For US citizens, a one year cost just under 1,000 Rmb per year, multiple entry.

Other types of visa, like a work "Z" visa, also requires you get a residence permit.  This one is granted on a year basis, but lately I have seen some issued for 9 or 10 months (length of work contract).  The permit is tied to your employer, so if you leave work, or change employers, you must get a new one to be "legal'.

And one last thing.  Please, do not confuse the "Residence Permit" issued by PSB ( you must pay for it) with the " Registration Form for Local Temporary Residence", which is done at the nearest Local Police Station from where you reside( it is free of charge), and also a must to have every time you enter China and do not stay at a hotel, but at a private residence.  Pay no attention to those that tell you not to do, not required.  If you do not, you may get in trouble if you ever need to go to PSB for any reason, they require to see your passport and Registration of Local Temporary Residence" prior to even say "NiHao" to you.

If still have any doubts, please post other questions.

HappyExPat, that is an exceptionally well-done post and very, very informative and based upon my own experience, quite accurate.