This is not necessarily the most important triceps exercise, but it's my favorite for pulling the horseshoe of muscle down the back of my arm, so my triceps look like a separate bulging twisted-steel bodypart of their own. Lying extensions offer a combined advantage of focusing heavy compound weight and concentrated stress into the triceps complex, without sapping energy to stabilize the rest of the body.
It is important to keep your elbows pointed straight up. Do not allow your arms to rotate at your shoulders. Doing so brings your chest and shoulders into the movement and robs your triceps of the extension. Think only in terms of extending your forearms vertically, with your elbows as the only hinge.
I get the best pump from these with six sets, 12 reps per set, in the following manner: do one set, release it, take a breath, do a second set, release it, take a breath and do a third set. After a brief shakeout, repeat that sequence.