"R" is the name of Rugal's black market organization/private army, as well as the short-name that Rugal sometimes signs letters with. Ultimately, "R" is not as big a player in the criminal underworld scene as Shadaloo or the Syndicate are, but can't be underestimated.
R operates out of a massive naval battleship called the Blacknoah. Powerful, loaded with structural redundancies, and equipped with an advanced Electronic Countermeasures package that makes it difficult to find on radar, the Blacknoah serves well as a mobile, well defended 'home base' for the group. Several jets and helicopters allow transit from this ship to various locations on dry land.
Their primary activity is smuggling illegal weapons and drugs. In fact, R is the world leader in these two criminal activities, outperforming even Shadaloo and the Southtown Syndicate in this regard.
On the other hand, R lags behind its rivals in other criminal venues and can't afford to maintain quite as large an army as some groups, making them a 'niche group' in some ways. Not that it stops them from trying other pursuits, mind you.
Lacking the control over politics and law enforcement that other groups have, Rugal and his group are forced to operate in the shadows, and when they do make a move in the open, they try to make it as short as possible.
Ultimately, Rugal is trying to take over the world through his "R" group. Some of his methods are rather diverse, and at times he ends up making curious choices; a side-effect of his major hobby.
That hobby is collecting statues of fighters. These aren't sculptures, but rather, Rugal invites talented fighters onto the Blacknoah and then either recruits them to his group, or defeats them in combat and turns them into bronzed statues. (On a major theme note, despite what the videogames Capcom vs. SNK, and KoF '94/'95 show, Rugal does NOT have a statue of Guile, since Guile is alive and well on MotM).
Rugal's group is fairly small, and there's only a few ways to join it for those suitably inclined. The most common way is Rugal inviting you to join, either by sending a letter, or just having Vice and Mature bring you to the Blacknoah, and then making his offer.