OLAP council was formed in January,1995 with the aim of setting a common platform for OLAP vendors and serve as Industry guide. The mission as seen on their website- http://www.olapcouncil.org/index.html.
The council came up with Multi-Dimensional Application Programming Interface (MDAPI) and its revisions to allow standardisation and interoperability between various OLAP products. Several vendors joined OLAP council including IBM, Business Objects and so on while Microsoft choose to stay away and launched its OLE DB Data access API with multi dimensional capabilities. Ultimately, OLAP council was shut down (though their website still exists) and was replaced by Analytical Solutions Forum (ASF) in October 1999 which was even more inefficient than OLAP council and soon passed away. Microsoft then became the pioneer in Business Intelligence world.
Too much of a dose of History...yeah? Lets bring on the floor Codd's rules.
Edgar Frank "Ted" Codd coined the term OLAP and gave 12 rules for online analytical processing. However, there is some controversy in the BI industry on the number of these rules as one can witness quite some redundancy in these rules.
Rule 1- Multidimensional conceptual view
Rule 2- Transparency
Rule 3- Accessibility
Rule 4- Consistent reporting performance
Rule 5- Client/server architecture
Rule 6- Generic dimensionality
Rule 7- Dynamic sparse matrix handling
Rule 8- Multi-user support
Rule 9- Unrestricted cross-dimensional operations
Rule 10- Intuitive data manipulation
Rule 11- Flexible reporting
Rule 12- Unlimited dimensions and aggregation levels.
Learnt from POD that dimensions usually are 5-6 and can go up to 12 ( not infinite as Todd stated!). He also mentioned that sufficient efforts must be put into handling sparsity of the data as the same algorithm might not be applicable in all scenarios.