Refers to the problem caused by exponential growth of hypervolume as a function of dimensionality. This term was coined by Richard Bellman in 1961.
As stated in Lecture 3 - Bayes classification_OldKiwi, The curse of dimensionality starts at d>17-23. There are no clusters or groupings of data points when d>17. In practice each point turns to be a cluster on its own and as a result this explodes into a high dimensional feature vectors which are impossible to handle in computation.