Your boiler heats hot water and pumps it through plastic pipes under the floor (or in some cases, behind the walls, or in a regular baseboard). The popular way is to heat the floor because it feels nice. It doesn't have to get hot, though. Just warm enough to make the air warm up around it.
Its kind of like the old school metal radiators, but instead of one little metal thing in the corner, its distributed all around the room. Because its got more surface area, it doesn't have to get as hot. It works better than blowing hot air, because blowing air means a filter, it means dust, it means losing heat in the ducts, and it means a physical fan that's pushing the air. Lots of moving parts that can break, not as energy efficient, and when the hot air comes out of the duct on one side of the room, its warmer than the air on the other side of the room, so you get hot and cold pockets.
A warm floor also conducts heat upwards to the room, and to the next floor, too, so you can set the temperature lower and get a nice even distribution of heat without the dry nosebleedy air you see with other kinds of heating. Which is nice for your baby and toddler because you might not need a humidifer for them as often. And if you have dust allergies in the family, its a lot nicer.
If you're looking at a home that already has it, its priced in to the home price, but it might be worth it. If you're looking to put it into an existing home, the costs can be a lot higher for obvious reasons.