Operations on data
Literally, a slice is subset of a cube corresponding to a single value for one or more members of the dimensions not in the subset#.
In practical, slicing is the way to work on facts limited to particular values in some dimensions. For instance, it would let you retrieving the sales amount for the years 2007 to 2010 only in America (quite equivalent to the WHERE of SQL queries).
Drilldown and Drillup
Drilldown and drillup are operations which consist of zooming in and out on a cube dimension.