If you have a mathematical background you are familiar with the idea of a function. A function maps the values of one quantity to those of another. For example, the number of candy bars you have sold in your shop is a function of how long your have been selling them. This simple example has one independent variable (time) and one dependent variable (number of units sold). Now, imagine you have several shops. Then you can construct a function of two variables, using both the shop and the time as independent variables. Doing so you could say how many candy bars were sold for this store at that time period. You can keep going, with more and more specific descriptions of the sales process to create functions of not just two, but several variables. The computer world calls the independent variables "dimensions" and the dependent variables "measures". This mapping of the multiple descriptions of the sales process (i.e. Time, store, product, etc) to the result of the sales process (number of units sold) yields a multidimensional measure. A multidimensional data model is a data model that is built around measures in this form. A "star schema" is the classic example. A star schema is a relational data model possessing a fact table with one column for each piece of descriptive information (dimension) and one for each measure. There are also specialized software products for accommodating data like this that give greater speed and computational flexibility (essbase, analysis services, oracle olap). The book, "The Multidimensional Data Modeling Toolkit" describes this in detail.
This model views data in the form of data cube. A data cube allow data to be modeled and viewed in multiple dimensions.It is define by dimensions and fact.