Most guys want big arms, so they focus on the biceps. But remember, the triceps make up the bulk of your arm circumference. Various aspects impact the speed in which your triceps can grow. I call them the "three P's."
Unlike biceps where the pump is more important than the pounds lifted, triceps need both. However, before you slap another plate on the bar for skull crushers, don't lose sight of the fact that heavy pressing movements for chest and shoulders invariably work the triceps. As such, the bulk of my "heavy" lifting for triceps is taken care of through chest training, not tricep-specific exercises.
Triceps respond extremely well to a fascia-splitting pump, which is best achieved via extended, giant, and drop sets. A great giant set example is: tricep pushdowns; followed by dips between benches; followed by close-grip push-ups. An extended set that I'm loving lately includes single handle pushdowns going from a supinate to pronate grip. Here's what that looks like:
Nothing halts triceps progress like inflamed elbow joints, which is why the order of your exercises is so important. I prefer doing tricep work immediately after chest and/or shoulder training.
Training triceps after heavy pressing movements ensures your elbow joint is warmed up and includes the added benefit of forcing you to lift lighter on triceps specific exercise – an extra safety feature.
Lastly, on the programming front always finish triceps with a stretch-focused exercise. I see quicker growth when a fatigued and massively pumped muscle is stretched. Think overhead extensions. Here's how they look in a superset with biceps: