A ticket is usually only good a single journey, and time-stamping keeps people from trying to re-use a ticket more than once. If an authority on the train checks your ticket, that time stamp tells him/her approximately when you got on the train. If your ticket isn't stamped, they'll fine you as they'll suspect you were going to try and use that ticket again (and there's NO arguing about it).
Also, if that ticket shows a stamp from, say, the day before, they'll suspect it's already been used once and fine you for that.
Tickets for regionale trains in Italy have a life span of 4 hours or so from the time they've been stamped to the time you have to be off the train (or at least on your way to your final destination.) Again, that's to keep people from just re-using the same ticket all day long or more than one day.
I'm unsure of the life span of a Circumvesuviana ticket but safe to say, validate it just before you board your train to your destination and then discard the ticket after you've arrived.