It seems a bit strange to start with learning about a tool, and then using it to define one's needs. Usually people come at it the other way and end up asking how.

In a nutshell, SSAS helps you build business intelligence solutions on top of a data warehouse. These can either be in the form of a traditional OLAP cube (which any number of ad hoc and reporting tools, including excel, can access), or a tabular model, which can be leveraged using sharepoint, excel, and power pivot.

Long story short, it helps you take a LOT of data and build very fast reports and/or ad hoc reporting/analysis capability to decision makers.