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