I moderate a Creative Mountain Dulcimer Community on Google+ to discuss the instrument and its possibilities. I also participate in other online discussion groups such as Friends of the Mountain Dulcimer.
About the Mountain Dulcimer
The mountain dulcimer is a fretted folk zither that is semi-indigenous to the mountainous areas of the eastern United States. The most complete history of the instrument of which I'm aware is Ralph Lee Smith's Appalachian Dulcimer Traditions. Evolved from older European instruments (especially, it seems, the German scheitholt), the dulcimer continues to evolve.
The "mountain dulcimer" most usually features a diatonic fretboard. That is, on any string you can only play all the notes of that open note's major scale with a substituted flat seventh (e.g., Mixolydian mode). Most contemporary models also include a major seven as well on the so-called 6 1/2 fret. This is not to say that you can only use a dulcimer to play music in Mixolydian or Ionian modes, however: far from it.
Beyond this, some dulcimer makers are starting to feature 1 1/2 frets on demand as well, and fully chromatic fret boards are also becoming more generally available. I've built several chromatic dulcimers and adore them.
The typical dulcimer is a zither — its strings are stretched across its body, which most usually extends the full length of the fretboard (as compared with lutes, where strings ride a neck that extends out from the body). Of course, there are dulcimer-related lutes as well, such as the strumstick.
Acoustic or Electric?
Generally, mountain dulcimers are acoustic instruments, but as with guitars, it's possible to build electric dulcimers, solid body instruments with magnetic pickups. Many acoustic makers also offer the option piezo-electric pickup systems on their instruments as well.