Amortization of Intangibles is the reduction of value of an non-physical asset over time. It is intended to capture, for example, the nature of a copyright to typically grow less profitable as time goes on.
In practical terms, an external analyst will only rarely need to separate this from depreciation; the income statement effects of them are typically what we care about.
Nonetheless, cases where intangible assets are material relative to physical assets might make this useful. Disney's copyrights comes to mind, and Coca Cola's brand is another.