The verb evince means to show or express clearly or to make plain. Evidence can evince the innocence of the accused, and tears can evince the grief of mourning.
Evince is a rather formal word that reveals the presence of something hidden — usually a feeling. So, if you are happy, your smile might evince your happiness. And if you are angry, the skull and crossbones on your tee shirt might evince your anger. Evincing is about expressing. If you are keeping your feelings inside, there's not a lot of evincing going on.