This question refers to "Buddhist Modernism" however I'm not sure what it is. It is a term that I have heard crop up in a few other places. Is it a reformation movement within Buddhism? If so what is it reforming and when did it occur? Is it particular to one school of Buddhism? Is it a related concept to Navayana Buddhism perhaps? Is it a real movement at all or just convenient shorthand for Buddhism as it enters the modern world?
Buddhist modernism is a scholarly (and increasingly, popular) term for the variety of ways that Buddhism has been adapted, both West and East, to recent (last couple hundred years) Western cultures, philosophies, societies and intellectual traditions. It includes (not an exclusive list):
- de-emphasis on ritual
- de-emphasis on the ultimate goal of nirvana or enlightenment in favor of lesser goals or even simply everyday relief of suffering
- emphasis on lay vs monastic practice
- re-invigoration of meditation as a major practice after long decline in some traditions, even among the monkhood
- identification with western values from the Enlightenment (in the western intellectual history sense) and Romantic movements
- alliance of Buddhism with science and scientific values
- adoption of the Western philosophical standpoints of naturalism and physicalism and corresponding de-emphasis on so-called supernatural phenomena such as rebirth/reincarnation and non-physical realms and beings
- reinterpretation in various ways of karma as a naturalistic phenomenon
See the Wikipedia article for more details and references.
Buddhist modernism just refers to Buddhists who only accept the aspects of Buddhism they consider to be compatable with the modern world. Usually the term is used to describe Buddhists who reject things like Karma and Rebirth but still see the Dharma as having things to offer. It's not a movement, just a catch all term used to describe people like that.
I think it is worth noting though that the term is relative to some extent. For one group of people it would be considered modernism to suggest that the traditional stories passed down aren't 100% accurate, and in other groups rejecting such stories might be the norm. I also think that there is a legitimate place for questioning and analyzing the core claims of Buddhism, although I think that the claims actually stand up whereas people who get called Buddhist modernists tend to think that's not the case for some of them.