It is often necessary to give additional information on a dimensional attribute in a hierarchy, although it may not be meaningful to use this information as aggregation criteria. 

For example, users may find it useful to know the address of each store, but they may hardly want to sort out sales by store address. 

Descriptive attributes represent this type of information in fact schemata.

A descriptive attribute is functionally determined by a dimensional attribute of a hierarchy and specifies a property of this attribute.
Descriptive attributes are always “leaves” of hierarchies.

Descriptive attributes are often tied to dimensional attributes by one-to-one associations so they do not actually add useful levels of aggregation (e.g., Address). 

Sometimes, they have domains with continuous values, so they cannot be used for aggregation at all (e.g., Weight).

A descriptive attribute can also be directly connected to a fact if it describes each occurrence of that fact, but it is neither possible/interesting to use it to identify single events or even to make calculations (otherwise, it would be a dimension or a measure, respectively).