There is typically one bathroom per train car on Italian trains. On newer trains, and especially high-speed trains, they are more spacious than what you might find on an airplane and offer the same basic features as those of a plane lavatory - a flushable toilet, sink with running water, soap, and paper towels.
On older trains, bathrooms can be significantly less accommodating. And, of course, there's no guarantee of any individual bathroom being clean or well-stocked when you use it. It's a good idea to carry a packet of tissues and hand sanitizer with you just in case.