An Acronym for Balanced Technology Extended although one suspects they made this a Backronym to follow ATX.
BTX is a standard for motherboards aimed to replace ATX.
The main benefit quoted for BTX over ATX is heat distribution. A BTX board is meant to passively dissipate heat (as opposed to use of fans) as much as possible. This is meant to make it suitable for TV/entertainment type devices such as ones used by MythTv.
Manufacturers have not made the switch as fast as happened between AT and ATX. Part of the reason for this is considered to be that the size of the motherboard is smaller which has presented some problems in design.