From a sociological point of view it could mean the assimilation of ethno cultural minorities in Sri Lanka such as the Sri Lankan Tamils, Colombo Chetties and indigenous Veddas into the majority Sinhalese identity. 
From a political point of view it could mean the Sinhala language favouring policies PS[›]of the post colonial governments of Sri Lanka that is considered to be a major cause  of the current Sri Lankan civil war. It is termed as culturo-ideological exclusivism by some which is a sense in which one's cultural values and norms are absolutised in such a manner that a particular way of life is enshrined as superior to all others and must therefore be adopted by others (e.g. the Tamil reaction to the perceived "Sinhalisation" processes of the Sri Lankan state)
The Term usage in India
Media in India use the word "Sinhalisation" for mentioning the process which the Sri Lankan government funded and sponsored settlement of Sinhala people in the Tamil dominant regions to make the places as multi ethic. Some reports claims that the Sinhalese and Sinhala military families are settled on the houses which are build by the money given by the Indian government for the welfare of the Tamil people. 
^ elite: The late President J. R. Jayawardene's first paternal ancestor was a Colombo Chetty and there is an excerpt from the biography of J.R. authored by Prof. K.M. De Silva & Howard Wriggins, in support of this. Don Adrian Jayawardene, J.R.'s paternal great-grandfather, descended from a Chetty family, but two or three generations earlier, a male of this family had married a Sinhalese by the name of Jayawardene from the village of Walgama near Hanwella and had taken on the name of Jayewardene and by the time Don Adrian arrived on the scene at the tail-end of the 18th century, the process of 'Sinhalisation' of his family had been completed.
^ PS: Sri Lanka’s nation-building programme became intimately linked with a Sinhalisation of the state directive. It was expected that the minorities would be assimilated into this new Sinhalese Buddhist nation-state. Moreover, the 1956 election marked the beginning of an era of ethnically-based party politics. 
- Susantha Goonetilleke, Sinhalisation: Migration or Cultural Colonization? Lanka Guardian Vol. 3, No. I, May I, 1980, pp. 22-29, and May 15 1980, pp. 18-19.
- Power and Religiosity in a Post-Colonial Setting: Sinhala Catholics in Contemporary Sri Lanka by R. L. Stirrat American Ethnologist, Vol. 22, No. 2 (May, 1995), pp. 428-429
- "History of the Colombo Chetties" by Deshabandu Reggie Candappa published in December, 2000
- "How it Came to This – Learning from Sri Lanka’s Civil Wars By Professor John Richardson". paradisepoisoned.com. Retrieved 2006-03-30.
- "Ethnic Identity, National Identity and the Search for Unity". World Council of Churches. Retrieved 2006-03-30.
- "Significance of the abortive 1962 military coup". Hindustan Times. Retrieved 2006-03-30.
- "The Human Rights and Humanitarian Fallout from the Sri Lankan Government’s Eastern Agenda and the LTTE’s Obduracy". UTHR. Retrieved 2006-03-30.
- "TamilNet: 23.04.13 Indian news magazine highlights accelerated Sinhalization of Tamil north". UTHR. Retrieved 2013-04-23.
- "Exclusive: Erasing the cultural leftover of Tamils to convert Sri Lanka into Sinhala country". UTHR. Retrieved 2013-04-23.
- "New military colonies in Murukandi; Sinhalization in Puthumathalan". UTHR. Retrieved 2013-04-23.
- "Salt on Old Wounds: The systematic Sinhalization of Sri Lanka`s North, East, the historic habitat of the Tamil speaking people". UTHR. Retrieved 2013-04-23.
- Sinhalization of the Vanni Mainland
- Colombo Telegraph
- Sinhalisation of a costal village in Puttalam district
- Sinhalisation of the Vedda community