Heres something in easier language....
Its a more direct way of mic'ing your drums... the trigger clamps to the hoop of your snare, tom, or kick drum, and there is a foam pad with sensors and wires in it that detect the vibration from your drum and sends that to a module, which in turn can be modified to give you the desired sound from your drums....
Some drummers view triggering as "cheating" because no matter how hard you hit the drum, it will still send the same volume to the speakers.... Also, triggers can give you a wider library of sounds you can play with when it is ran through a module (Roland usually is you best bet)
Now for compaines, I have heard that Rolands are a bit more reliable that
ddrums (I was talking with Kevin Talley after a Dying Fetus show and he told me he broke his
ddrum triggers while on tour, and he tried getting replacements from
ddrums headquarters and was not able to, he says it took him about 2 months to get replacements) Also,
ddrum makes two (I believe) differant qualities of their triggers
here is
ddrums triggers
ddrum - Acoustic Drums and Electronic Drum Products since 1983
hope this helps
