The way he stared deep into her eyes was making her uncomfortable. For a first date, this was too much intensity. Intensity is the degree, volume, or magnitude of a thing, such as fire, emotion, weather, work, or passion.
Intensity is a word sometimes associated with passion, fire, and violence. It's used when discussing the level of such things as a love affair or, perhaps, a flame. For example, the intensity of the relationship between Bergman and Bogart in Casablanca was very high. Likewise, meteorologists measure the intensity of tornados on the Fujita Scale. Some things are meant to show intensity, such as performance by a great musician. Other things, such as, say, a blanket...not so much.