Nationalism, in general, refers to a strong sense of identity with one's nation. It means supporting the perceived national interest of one's country to the extreme exclusion of any others.
Beginning in the nineteenth century, being of a certain nationality, such as Greek, Serbian, Bulgarian, or Russian, became closely associated with membership within the Eastern Orthodox Church. You probably have noticed that individual Eastern Orthodox congregations identify with a particular nation. In this sense, nationality and religious affiliation became one and the same. While dogma tends to remain mostly standardized across the Eastern Orthodox Church as a whole, regional differences have arisen. Often, saints of a particular nationality are given particular emphasis.
While this has served to strengthen bonds between worshipers of shared nationality, it has also led to some problems within the Eastern Orthodox Church as a whole. Sometimes, nationality is given more emphasis than spiritual practices. This became the case when during the most recent conflict in the Balkans when many Albanians and Serbs refused to worship in each other's churches. This also caused strife after the fall of the Soviet Union when Russian nationals in Estonia wanted to remain under Russian church authority. Naturally, ethnic Estonians wanted to restore their own ecumenical authority.
The nationalistic nature of the Eastern Orthodox Church has also made attracting converts difficult. Many who are not ethnically associated with a traditionally Eastern Orthodox nation find themselves to be perpetual outsiders, no matter how strong their faith. This has also complicated matters in multiethnic countries such as the United States. Because the Eastern Orthodox Church has no common expression of faith that transcends its many nationalities, many people without strong nationalistic feelings find it hard to find spiritual relevance.