The original application of the magnetic horn was in the context of neutrino physics, where beams of pions have to be tightly focused.
Production of a neutrino beam generally involves directing protons onto a fixed target of solid material.
The protons interact strongly with the nuclei in the target, producing a variety of secondary hadrons.
The shape of the horn and strength of the magnetic field can be tuned to select a range of particle energies that are to be best focused.
Note however that the decays of the secondary hadrons still impart some random direction to the neutrinos, so the beam will always spread to some degree no matter how well the horn works.