"Western medicine" is a term sometimes used to describe evidence-based medicine, which, for various historical reasons, emerged from "Western" civilisation (i.e. countries originally populated by or settled by Europeans), though it is now practised throughout the world.
The term is most commonly used by promoters of "Eastern" medicine or therapies, such as acupuncture or Reiki, or of other forms of alternative medicine. It may be substituted for other phrases such as "conventional medicine" or "mainstream medicine" by promoters of Western forms of alternative medicine, such as homeopathy. You're most likely to encounter these terms in the context of explaining how Western medicine only focuses on symptoms and not the causes of illness, or some other such hogwash.
Although the phrase "Western medicine" is not actually inaccurate as such, since the theory and practice of empirical medicine developed most prominently in Western countries, it can be misleading since it tends to imply that evidence-based medicine belongs to Western culture, in the same way that traditional Chinese medicine belongs to Chinese culture, for example, and that it's therefore no more valid than any other system of diagnosis and treatment.
Both suggestions are false. The defining feature of what is termed "Western medicine" is its efforts to base itself on the scientific method and on knowledge and techniques supported by rigorous scientific research. Hence it is rooted in empiricism rather than culture, although of course there is variation throughout the world's cultures regarding attitudes to empiricism and alternative worldviews such as religious or spiritual ones.
One holistic website bashes humorism and bloodletting as being barbaric, unscientific, "Western", and akin to allopathy, and simultaneously praises traditional Chinese medicine and its (also unscientific) system of qi, meridians, and yin and yang. The writers are obviously unaware of the fact that bloodletting is still used in traditional Chinese medicine.