None of the replies so far give a clue as to what "black money" is.
It's actually not a popular concept, but from the little I understand, I'd try to make it somewhat understandable, this is best excerpt I could surf on the internet on what black money actually means:
What is black money? The National Board of Revenue(NBR) defines it as any legally or illegally earned money which is not declared to the government agency, and on which no income tax is paid to the government. This definition tends to dilute the seriousness of the matter, because it minimizes the importance of the concept of illegally obtained money or unearned income or money amassed through immoral, improper and illegitimate means. Black money is linked to corruption, crime, illegal activities and the black economy. A perhaps more accurate description of black money revolves around the concept of money illegally obtained through political and/or bureaucratic corruption, bribery at all levels of the government, semi-government, autonomous or semi-autonomous offices or organizations, as well as money amassed by business people through smuggling, black marketing, shady deals, profiteering, money amassed by labour leaders, student leaders, through extortion – and especially, money amassed by functionaries of the ruling government party and its various organs, and their families, relatives and cronies.
So based on the foregoing and the explanation of what black money actually is above, "whitening black money" means declaring such assets to the government, making them aware of it, but the source and legitimacy of such funds would not be questioned cause the owners will be charged a certain percentage in tax, so it basically just works like this: you make known money the government has no idea of, money they have previously charged no tax on, you then pay tax on them, integrating it back into the normal, everyday, "white" economy, this act to an extent frees you of criminal charges and the rest. Thus that's why my earlier post criticizes such scheme, as I believe it just favors the criminal-minded government and some of its capitalist organizations to keep embezzling money and getting away with it.