Engaging in mindfulness implies changing what you think about, or, where your focus is. This can be therapeutic to persons who are suffer from anxiety and depression because it interrupts periods where negative thoughts dominate their consciousness and replaces them with periods where their thoughts focused on current circumstances that are generally benign or pleasant. For persons who don't benefit from such therapy…
The lack of rigorous scientific support for this assertion is the entire point of this article (and the journal article it summarizes).