The RIAA is short for the Recording Industry Association of America. In the RIAA's own words on their website, they are set up to "foster a business and legal climate that supports and promotes our members' creative and financial viability." In other words, they are an advocacy group that lobbies for laws and business practices that make collecting profits easier for their members (and by extension, the US music industry as a whole).
By and large, the RIAA membership is made up of record labels. All major labels are members and many independent labels belong as well. Aside from record labels, some individual artist catalogs are "members" of the RIAA, usually via a publisher. More than 90% of the music sold in the US comes from RIAA members, according to the group.
The RIAA is actively involved in government lobbying whenever legislation comes up that might impact the music business, especially First Amendment issues. On their website, they also provide resources for parents looking for information about the music their children are listening to, current guidelines for parental advisory stickering and more. Their real mission, however, revolves around intellectual property rights and copyright control. The group has worked with the FBI to develop new anti-piracy stickering and warnings and is intensely involved in coming down hard on internet file swappers.
If there is one reason your average member of the public knows about the RIAA, it's because of their digital downloading lawsuits. They have vigour sly, to put it mildly, pursued people who have used P2P file sharing networks and slapped them copyright infringement lawsuits (although not all labels have been so grateful for the "help"). This is the RIAA's burning issue and is central to the work they do.
If you would like to join the RIAA, you must have a registered record label in the US - there are no personal memberships. You must submit an application and copies of some of your releases, and if approved, you will be asked to pay dues that are determined based on your level of sales. You can find the application on their website.
