I interpreted the question as asking for an explanation of how elementary particle collisions lead to cascades of other particles.

Why this is possible is simple: it is possible to convert the kinetic energy of the collision into particles by means of Einstein's E=mc^2.

How it happens is a little harder to explain for laymen, but I suppose we could get away with Feynman diagrams.

We have met the enemy, and he is us — Pogo