Neck-Through-Body construction is virtually indestructible: it means that the neck extends all the way through the guitar instead of being either bolted on (Bolt-On) or glued into (Set-Neck) the body.
The "body" of the guitar is actually comprised of "wings" that are attached to either side of the Neck-Through section of wood. This guitar construction method provides the least resistance to the vibrations produced when the instrument is played, resulting in a rich, thick tone and extended sustain.
You will likely spend more for a neck-through-body guitar because they are more expensive to build. Examples of neck-through-body guitars are the high-end Jacksons like the Solist, Ed Roman's Abstract Guitars, and Ibanez makes a nice X series neck-through model.