What is a Rail Pass?

A rail pass is a special ticket which gives you unlimited train travel on the national rail network of one or more countries, so you can travel around freely
Rail passes for a specific country/region are only available to international visitors with foreign passports. You can’t buy a international rail pass for the country you live in.
A pass is generally worth it if you're going to make a number of long-distance train trips; in some countries it can be great value as separate train tickets can sometimes be expensive.
If you're prepared to avoid the rush hour peaks, and especially if you book cheap tickets in advance (subject to the rail company’s terms and conditions) then point-to-point tickets may be cheaper than a pass.
Unlimited means you can simply hop on any train you like, find an empty seat to sit in, and show your rail pass when asked. Seating reservations are generally required for popular high speed trains.
Train staff may check your residency so make sure that you bring the right documents.
Depending on age, validity and number of countries, prices can vary considerably, so read the SMALL PRINT.

Is a railpass cheaper than buying point-to-point tickets? It depends.

If you're only making a few short journeys, you're almost certainly better off buying ordinary point-to-point tickets on the day.
For a pre-planned fixed-itinerary trip, the cheapest option is usually to buy cheap advance-purchase point-to-point tickets online direct from the European train operators.  There are great bargain train tickets available up to 3 months in advance.  So don't buy a pass for pre-planned trips before checking what cheap ticket fares first.
For long-distance spontaneous trips, passes do give you the flexibility to change plans as you go. In Europe, seat reservations are sometimes compulsory and can cost between €3-10.
The only way to know for sure whether a rail pass or point-to-point tickets would be cheaper is to work out the point to point prices for most of the trips you're planning (use the direct train operator websites, not ticketing agencies which often ignore the cheap deals).
Don't be afraid to mix & match a rail pass with point to point tickets. 

What trains does a rail pass cover?

Rail passes cover all the trains run by the main national train operator in each country
Local, suburban & regional trains usually don’t require seat reservations or surcharges.

What trains does a railpass not cover?

Rail passes do not cover metro (underground /subway) trains or trams.
Rail passes don't cover Eurostar (but Eurail/ Interrail Pass Holders can get a discounted fare if you buy your tickets at the station).
Many premium daytime trains require rail pass holders to pay a small surcharge and/or make a seat reservation.
You pay extra for sleeping accommodation (couchettes, beds, sleepers) or the use of cabins, berths and reclining seats on board.
Seat reservations are generally non-refundable and non-exchangeable.

Seat Reservations

In Australia, Canada and US seating reservation are generally compulsory for long distance trains, and can be done with no extra charge.
In Europe, some local, regional slow speed trains don’t require seating reservations.
However, they are required for international city-to-city routes, inter country city routes, night trains or popular high speed trains between a e.g. ICE or IC trains.
Seat Reservations not included in the cost of rail passes, costs between €2-8 and can be made for up to 90 days before travel.
This can be done mainly at the train stations.
Seating Reservations can be avoided by using slow speed domestic trains in say Austria, Belgium, Denmark, Germany and The Netherlands
Check with selected country to see if there are any seating reservations to be paid.
The price you pay for a seating reservation can also be called a supplement.
It normally costs the same for booking 1st/2nd class seating.

Supplements  

You must make a reservation for a night train and for sleeping accommodation, you must pay a supplement.
You can reserve this in advance through a travel agent, at station or rail call centres
Sleeping supplements can cost anything between €20-100, depending of choice eg. couchette, bed or private sleeping room.