It's Hnda's high performance version of their cars, Type R. Like the integra/Civic Type R, NSX type R, as opposed to LX, EX, SI, the R is the factory's racing effort. For the domestic guys think of it as Chevy's SS, Dodge's R/T, Ford's SVT.
But I guess it can relate to their bikes too. They started with the CB's and now they got CBR's.