A ticket gives you the right to travel between two points. A reservation books a seat.

The overwhelming majority of the world's train journeys don't guarantee a seat (think commuter trains for example). On most European inter-city journeys, reserving a seat is possible but most of us don't bother. Life's too short to faff about committing to taking the 1820 when the only downside, should we choose to take the 1850, is the sl;ight possibility of having to stand for the first couple of stops. On a few (mostly high speed) trains, reservation's compulsory - and reservations are often part of discounted, generally inflexible, advance booking deals

It's likely that the train you're looking at allows reservation and possible that it's advisable to reserve. It's also possible that reservation is impossible.

Advise this forum of what train you're looking at at someone more knowledgeable about the details of Italian trains will advise

A

In Italy (or on Trenitalia), all trains tickets except the slow R trains will include your seat reservation. The slow R trains don't have reserved seating at all and there is no point in buying R tickets in online as there are more restrictions than bought at the station. For the faster trains (AV,ES, ESCity, IC), there are advance purchase discounts so you can often save a lot of money buying on Trenitalia online. R train tickets need to be validated before boarding. Other tickets with seat reservations don't need to be validated (they will be checked on board).

In other countries, seat reservations often aren't mandatory.

Scroll down through this thread until you get to the information about how to register on Trenitalia. Be sure and register before purchasing and notify your credit card in advance.
http://www.roninrome.com/transportation/booking-online-using-the-trenitalia-website-updated