Everyone is surprised to find out that I live in a tiny house by preference. 
I have seen shows advertised about tiny homes, but I really do not know much about them
They are a return to a frugal way of living. The small house movement is what its called. Basically members of the movement are saying we don't need a big house, we don't need a big space or items to live our lives. Most also pair this with a love of travel and desire to be more in nature. 
I guess it would be pretty thrifty in regards to energy usage.  I can imagine a pretty small utility bill
That's one perk! Also it's the fact that the average size of new single families home grew during 1978-2013 even though average family size decreased.  
I do wonder how someone can live comfortably in those things.  They seem like it would be a bit cramped, even with just one or two people
That's true. I think a lot of people use them as basically just sleeping areas. Some tiny houses are on wheels. The people that live in these houses can travel with them, sleep in them and have what belongings they have while making it less attractive to stay inside all day!
So they are more like a fancy camper trailer?  I guess there are worse ways to travel then.
Sort of. It's all about preference after all. Many people find tiny places more cozy!
I can see how it would fit a minimalist lifestyle.  No chance for much hoarding in a place like that!