When you heighten something, you increase it or make it more intense. If you want to heighten awareness about homelessness, you might write an article for your local newspaper.
Extreme weather can act to heighten people's concern about climate change, and publicity for a good cause can heighten awareness of the ways college students can volunteer their time. A movie director might heighten the tension in a scene by using scary music and dramatic lighting. In all of these cases, something is intensified or increased. The oldest, fifteenth-century meaning of heighten, however, was "to exalt, honor, or raise to a high position."