What exactly is a "trials" bike? I'm interested in learning more about trials bikes.  I've seen them in pictures and videos with the riders doing really impressive stuff on them; incredible balancing, huge jumps, etc. 

This type of riding is new to me and seems very fun (sort of reminds me of bmx riding as a kid).  My regular routine consists of mainly road and cx riding on normal frames with 700c wheels. 

I like to do balancing work and jumps on my cx bike, but there is a limit.  The wheels are large and harder (I imagine) to get off the ground than a smaller wheel.  Also, although I treat my cx bike pretty rough, and bang it around, I don't want to crack a carbon frame trying to land a big drop (or jump, or whatever).  

I'd love to start riding one of these trials bikes, however, I don't know much about them or what even makes a "trials" bike.

I basically know that:


they don't have a seat post or saddle
The wheels are smaller than a 700c wheel, some 20", some 24", some 26"?
they look superficially like a bmx bike


So my question is what makes a "trials" bike, and, what are the most important features to consider when either buying a used one, or building one myself?  I'm specifically interested in the wheel sizes ( why choose one over another ), dropout types and rear spacing.
Trials bikes were originally just mountain bikes, at the time most mountain bikes had 26" inch wheels and 135mm rear dropouts (trials is basically shorthand for mountain bike trials). Trials bikes of this design usually fall into the "stock" category.

When people started modifying bikes to be even more well suited for obstacle courses, the 20" wheels and 116mm rear dropouts were introduced, this is when the bikes started to closely resemble bmx bikes. Trials bikes of this design usually fall into the "mod" category.

"Stock" bikes and "mod" bikes make up the two officially recognized categories of trials bikes, so, plan for 20" wheels or 26" wheels. The 20s are generally more nimble but the the argument for 26s is probably more clearance and better balance.

There's quite a bit more information on the subject:

https://en.wikipedia.org/wiki/Mountain_bike_trials

http://www.biketrials.com/intro/what.shtml