Emotional intensity simply means that highly sensitive people tend to experience emotions on a much deeper level than non-sensitive people. So for example when they're happy, you might see them with a big smile on their face, acting silly or giggling a lot. When they're sad it seems like their sadness is a lot deeper than usual, or if they are upset you might see them cry. This is often puzzling to people who are non-sensitive. It is important to note that emotional sensitivity is not necessarily a bad thing.