The state representation is the definition of the state vector parameters. The default RecPack representation (RP::default_rep) is the RP::pos_dir_curv representation, which contains position (3 parameters), direction (3 parameters) and charge over momentum (1 parameters). It has dimension 7: x,y,z,ux,uy,uz,q/p.
There are other representations available and they should be used dependening on the needs. For example the RP::pos_dir_curv representation cannot be used in general for track fitting in a partcle detector because in general the sense of propagation of the particle cannot be determined from the fit. Thus a representation with no sense information should be provided. This is the RP::pos_slopes_curv representation, which substitutes the direction vector, with 3 components, by the slopes vector, with two components.