Intensity is about being adamant about a certain thing. It is about being clear in your mind what you are about, what you are not, and protecting that framework.
Intensity and passion are sometimes confused. Passion usually has a positive or happy connotation. Intensity doesn't have a positive or negative connotation - it just means a person or a message has strong voice or force.
Intensity does different things to different people. Some people will inevitably like your intensity and some will stay away from it. Those that agree will likely be your biggest supporters and those that don't will be your biggest detractors.
What you are intense about is a function of what gets your emotions going. For some people that's what gets them emotionally positive (happy) and for some it's what gets them emotionally negative (angry). I think both are equally powerful in producing strong intensity; in many ways, anger is likely a more powerful emotion than happiness.
A leader with intensity is very likely a good thing. That leadership style is a mark in the sand on the character of that leader. It is also authentic as it is the core emotion of the leader. It is also very clear as to what matters to the leader.
Intensity can be manifested in action and/or speech. The perfect alignment is with both, since one without the other seems misaligned. This misalignment can be construed as inauthenticity.