While furnaces distribute heat through warm air (via fan and ducting), hydronic heating systems distribute heat through hot water (via pipes/tubes and a pump).
Residential boilers typically run on natural gas or oil.
In floor heating systems warms up a room by heating the floor directly rather than warming the air in the room.
The heat form the radiant floor heating is absorbed by other objects in the room, helping to warm the entire space efficiently.
Water systems are typically recommended for new-construction projects in which the system will serve as the primary source of heat throughout the home.