To evanesce is to fade slowly out of sight. When something evanesces, it disappears.
Evanesce comes from a Latin term for vanishing, and that's exactly what it means. When something evanesces, it vanishes and is gone. However, this isn't a quick disappearing act; evanescing is gradual and takes a while. As you fly in a plane, the ground gradually evanesces. In a spooky movie, a ghost may slowly evanesce and fade away. A rainbow doesn't stick around for long; it eventually evanesces. Something that is prone or likely to evanesce can be called evanescent.