Degenerated Dimension is a dimension key without corresponding dimension. Example:
In the PointOfSale Transaction Fact table we have:
Date Key (FK) Product Key (FK) Store Key (FK) Promotion Key (FP) and POS Transaction Number
Date Dimension corresponds to Date Key Production Dimension corresponds to Production Key. In a traditional parent-child database POS Transactional Number would be the key to the transaction header record that contains all the info valid for the transaction as a whole such as the transaction date and store identifier. But in this dimensional model we have already extracted this info into other dimension. Therefore POS Transaction Number looks like a dimension key in the fact table but does not have the corresponding dimension table.
Therefore POS Transaction Number is a degenerated dimension.