Strictly speaking, the term "Eurasian" may refer to one of two things. The first definition pertains to a person from Europe or Asia, especially in the regions where the demarcation between the two continents is vague. The second refers to a person of combined European (Caucasian) and Asian ancestry. The latter is the definition mostly used today.
Taken in the contemporary context of a person with mixed ethnicity, the term "Eurasian" most likely originated from British colonizers who settled in India. Children born of Anglo fathers and local mothers were called Eurasian. Nowadays, the term is an umbrella for all individuals whose racial heritage is taken from both the west and the east. Filipino-White mestizos, Thai-White luk kreung, and even the Hawaiian Polynesian-White hapa can all fall under this category.
Statistically, although there is a considerable number of Eurasians or Anglo-Indians in India, the largest population of Eurasians in the world can be found in Southeast Asia. European colonizers left people of Spanish, Dutch, German, Portuguese, and French ancestry in this region, especially in the Malay peninsula. In some cases, these people have formed separate and tightly-knit communities, with their own traditions and cultures, perhaps due in part to the initial distrust given them by locals and foreigners alike.
Examples of these communities include the Kristang or Cristao of Malaysia and Singapore (Portuguese and Malay) and the Macanese of Macau (Portuguese and Chinese). Such groups have maintained distinct languages and cuisines and are likely to marry from within their own social subset.
In the more recent past, especially in places touched by war, children with mixed western and eastern features are looked down upon because they are seen as the children of soldiers and prostitutes - children of the nightmares of war. Perceived as constant reminders of hard times, these "G.I. babies" grow up unaccepted and shunned by local society. In fact, it was only in the 1990s that a lot of racially mixed Thais were even granted citizenship.
Interestingly, it seems the tables have now turned. Eurasians have become hot commodities in most fields which revel under the public eye and flourish as models, actors, entertainers, etc. The Eurasian face has now become de riguer in many Asian countries. In the Philippines, for instance, with its long history of Spanish colonization, Eurasian features have become the standard of beauty. The fair skin, tall stature, and aquiline nose are almost prerequisites for a career in the entertainment industry. This sentiment can be seen echoed all over the region, resulting in the Eurasians' relatively small population being over-represented in the media.