A slice is a subset of a multi-dimensional array corresponding to a single value for one or more members of the dimensions not in the subset. For example, if the member Actuals is selected from the Scenario dimension, then the sub-cube of all the remaining dimensions is the slice that is specified. The data omitted from this slice would be any data associated with the non-selected members of the Scenario dimension, for example Budget, Variance, Forecast, etc. From an end user perspective, the term slice most often refers to a two- dimensional page selected from the cube.
from OLAP Glossary, 1995