Many trains have different seating classes in different cars. There is a price difference, which you'll notice when you're browsing ticket options, and the higher prices in higher classes come with certain amenities.
The amenities and features of trains vary quiet a bit depending on the type of train you're taking. Most high-speed trains in Italy, for instance, are air-conditioned and have electrical outlets at each seat in all seating classes. Some trains only have second class seating, so even if you are holding a first class rail pass you'll be riding second class on those trains.
It's important to keep in mind that the difference between the seating classes on trains in Europe is not as great as the difference between classes on an airplane. Also, remember that some rail companies have given their seating classes names other than simply "first" or "second." You can typically figure out which of their unique names is "second" class by looking at the least expensive tickets, but when in doubt, ask.
First Class Seating
First class seats are typically larger - there may be two in the space of three second class seats, so each first class seat is wider - and offers more legroom. Most seat backs in first class recline, and some even have retractable foot rests.
The cars that are dedicated to first class seating are less cramped, since there are fewer passengers per car, which means there's more room to store luggage. In addition to the usual overhead racks and end-of-car storage, there are also often spaces between seats when they are positioned back-to-back.
Many first class trains come with a complimentary snack and drink (juice, soda, coffee) when you are first seated, along with a complimentary newspaper. First class cars are generally occupied by foreign tourists and European business travelers.
Second Class Seating
Second class seats are narrower than first class, and may even be bench-like seating on older or slower trains. Sometimes second class seats recline (more often on newer, high-speed trains), but not always.
Because there are more seats in a second-class car, and because most Europeans travel second class, these cars are more crowded. There's less room for luggage storage, though the overhead racks are always an option. Not all second-class cars have end-of-car luggage racks, and many don't have any other in-car storage besides the overhead racks.
Second class cars are generally occupied by the majority of European travelers as well as backpacking tourists.