A ragged dimension is one of the database dimension hierarchies where there is at least one member whose logical parent is not in the level that is immediately above it.
Consider a database of cities, states, and countries. San Francisco is in California, which is in the United States. This works well for most things, however there are instances where a country is not divided up into provinces or states (for example its just Geneva, Switzerland - Switzerland is not split up into states) or when a city is not part of a state (such as Washington DC).
When designing databases, this is generally avoided (though sometimes it is unavoidable). Such structures within databases cause odd numbers of rows to be returned when transversing the tree. This in turn may cause applications expecting three (in the above example) things back (city, state, and country) to break unless it is handled properly. Support of ragged dimensions (along with others) is a commonly touted feature of OLAP applications.
This term comes up most often in OLAP (On-Line Analytical Processing), though ragged has been seen in other places within computer science. Similarly related is the concept of ragged arrays (though this is not necessarily an OLAP term). The ragged dimension differs from an unbalanced dimension where the tree is not balanced, though there are no 'jumps' within the data - its just lopsided.