Rapidity is used to express angles with respect to the axis of the colliding beams, which are well-defined for particles travelling close to the speed of light. When particles travel at high velocities, angles defined in more familiar ways can grow or shrink, making discussion of these quantities difficult. Rapidity has the value 0 for particle trajectories that are perpendicular to the beam, and positive or negative values for those at an angle to the beam.
Pseudorapidity is an approximation to Rapidity. This quantity is sometimes used instead of Rapidity as it is easily calculated from the cartesian angle between the particle direction above or below the beam line and has a direct relationship with detector components. This quantity is precisely equivalent to Rapidity for massless particles.