A ragged hierarchy occurs when a dimension has branches with different numbers of levels. For example, a Sales Regions dimension has branches for North America and for Europe. Both branches have member level attributes for Country, State, and City.
The North America branch has United States, Massachusetts, and Boston. The Europe branch has Greece, Athens because Greece does not have individual states like the United States. The State level for Greece is empty, causing a ragged hierarchy.
Geographical dimensions and product dimensions often have ragged hierarchies.