First of all, what is a dimension ? Wikipedia defines a dimension in the Business Intelligence world as
A dimension is a structure that categorizes facts and measures in order to enable users to answer business questions. Commonly used dimensions are people, products, place and time. (Note: People and time sometimes are not modeled as dimensions.)
The definition in the Process Mining domain remains the same. A dimension is a way to analyze a process in a specific facet. For example admitting we’re analyzing an Order To Cash Process, it could be interesting to analyze only the orders which are processes in a specific region. In this example the concerned region will be the dimension (or the facet filter).
Imagine we can for example split the global duration of the analyzed process by the location dimension. By this way the analyst could for example analyze in detail and for each dimensions (Omaha, Chicago, etc.) how, in term of duration, the orders are really performed