A dimension is a structural attribute of a cube that is a list of members, all of which are of a similar type in the user's perception of the data. For example, all months, quarters, years, etc., make up a time dimension; likewise all cities, regions, countries, etc., make up a geography dimension. A dimension acts as an index for identifying values within a multi-dimensional array. If one member of the dimension is selected, then the remaining dimensions in which a range of members (or all members) are selected defines a sub-cube. If all but two dimensions have a single member selected, the remaining two dimensions define a spreadsheet (or a "slice" or a "page"). If all dimensions have a single member selected, then a single cell is defined. Dimensions offer a very concise, intuitive way of organizing and selecting data for retrieval, exploration and analysis.
from OLAP Glossary, 1995