The Presentation Layer determines what's shown in the user's screen, and how he can interact to ask new questions. There are many ways to present multidimensional data sets, including pivot tables, pie, line or bar charts and advanced visualization tools such as clickable maps and dynamic graphics.
The Dimensional Layer parses, validates and executes Multidimensional Expressions (MDX) queries. A query is evaluated in multiple phases and the axes are the first to be computed, right before the values of the cells within the axes.
The Star Layer is responsible for maintaining an aggregate cache. An aggregation is a set of measure values (cells) in memory, qualified by a set of dimension column values.
The Storage Layer is a Relational Database Management System (RDBMS) and is responsible for providing aggregated cell data and members from dimension tables.