It describes the economic fluctuations of approximately 50 - 60 years in length. My recent work has concluded that these fluctuations are actually caused by fluctuations in population growth. Because of the unevenness in population growth, social and economic conditions are affected. If you take the decennial rate of change of population, decade over decade, a cycle of 50-60 years in population growth appears. This is noticeable in U.S. population from 1789 onwards, but most noticeable in Canadian population.
Most economists know about the longwave.
The great debate since Kondratieff has been the empirical evidence for its existence and its causes. Those that write about the longwave today are those that are involved in economics, and the social and political sciences. This is the brief explanation. I hope this helps. A longwave mailing list will be starting soon.