Advanced calculated metrics aka Derived metrics allow to apply a segment to a metric and use it as a new standalone metric in Analysis Workspace. For example, you want to have a metric showing the number of visits from social networks, or bounce rate for mobile traffic, or orders placed only by new customers. The advanced metrics is a great way avoiding necessity of applying segments every single time.
The metric definition is not limited by combining existing metrics, dimensions and segments. You can also use variety of functions. For example, you can use If, Greater than and Percentile functions for building so called Weighted metrics like Weighted Bounce Rate that is used to ignore low-traffic pages.