My clients train hard. They don't scream or throw weights - they just push hard, trying to get more out of themselves than their bodies want to give, trying to walk that terrible, beautiful line between controlled aggression and all-out insanity.
Strictly speaking, intensity in the weight training context refers to the amount of work required to achieve the activity and is proportional to the mass of the weights being lifted - that is, how heavy the weight is relative to how strong you are.