Definition
MOLAP (Multidimensional Online Analytical Processing) is a format conceived especially for storing multidimensional data in a multidimensional database.
Use
MOLAP is an alternative physical store to ROLAP (Relational Online Analytical Processing), which is a store for multidimensional data in a relational database.
You have the option in BW to create aggregates either on the basis of a ROLAP store or on the basis of a MOLAP store. Scenarios, where both store types appear, are not possible.
Nevertheless, you can toggle between MOLAP and ROLAP aggregates.

You can find additional information about using and maintaining MOLAP aggregates in
Restrictions when using the MOLAP store
The BW MOLAP store is a platform-specific means of optimizing query performance. It uses Microsoft Analysis Services and, for this reason, it is only available for a Microsoft SQL server database platform.
To find out additional information about which conditions BW InfoCubes must meet to be modeled using Microsoft Analysis Services, see
Conditions for BW InfoCubes.Structure
The multidimensional data are stored in arrays in a MOLAP store. These arrays are physically stored as compressed files on the Microsoft Analysis Server.
In a ROLAP store, however, the multidimensional data is stored in tables that are organized in a star schema in the database.
Integration
The following overview illustrates how Microsoft Analysis Services is technically integrated in a Business Information Warehouse System.

The following services are also installed on the database server:

The SAP MOLAP Bridge provides the interface used to access Microsoft Analysis Services functions from the BW system.
See also:
BW Customizing Implementation Guide
-> Business Information Warehouse -> Connections to Other Systems -> Microsoft Analysis Integration ->