What does it mean if my penis gets big when wearing protective stuff like cups?

You're normal: No two guys get hard from exactly the same kinds of stimulation. It's cool to be involved in sports, wear body armor, and remember how important that thing is. Different guys get erections from anything from riding the old Chicago elevated train system to hearing the national anthem to the climax of a church service -- Love takes many forms, and you should enjoy whatever excites you.