Orthodox Jews are a subset of Judaism who are generally more religious and follow the traditional restrictions of the religion more strictly than other types of Jews (Reform jews, etc).
Their branch of Judaism largely has its roots in Eastern Europe and can now mostly be found in Israel, USA, Canada, South America and Western Europe.
They refer to themselves as Haredim. While modernized Jews who have reduced the strictness of their beliefs normally dress like other people, many Orthodox Jews dress distinctively and one can often tell the sect based on their particular style of clothes.
Orthodox Christianity is the Eastern branch of Christianity which split with Western Catholicism (and later Protestantism) in early medieval times. It was the church of Byzantium, the Eastern Roman Empire.
It has gradually split since then, especially in the late Ottoman empire where the Orthodox Christian nation (Millet-i-Rum or Roman Millet) was split into smaller sections in an attempt to deal with the rise of ethnic nationalism. As modern nations developed, they separated their churches so today you will have the Russian Orthodox, Serbian Orthodox, Greek Orthodox, etc churches. Note that people may be members of those churches while living outside of that country, so that there could be a Serbian Orthodox church in Canada or a Greek Orthodox one in Lebanon.
Hope this helps!