Being a catalyst for something means to be an agent of change, and the four crossword solutions all reflect this idea. To 'SPUR' something is to motivate it, to 'ACCELERATE' it is to speed up its progress, to 'INCITE' it is to provoke or stir it up, and to 'usher in' it is to bring it about or introduce it. Together, these words suggest that being a catalyst for something involves motivating, speeding up, provoking, and introducing change.