Analysis Services in SQL Server is used for Businness intelligence where the data is made available for Reports which is Pre-Aggregated by using the Cubes.
The Data mostly used for Cubes is always De-normalised OLAP Data. This Data is in either in Star Schema or Snowflake schema.
In Star schema the dimensions are normalized with each dimension represented by a single table in a Star like Structure.
In Snowflake schema the dimensions are normalized into multiple related tables.
A complex snowflake shape is where the dimensions of a snowflake schema are elaborate having multiple levels of relationships. The child tables have multiple parent tables.
The “Snowflaking” effect only affects the dimension tables and NOT the fact tables.