It is also known as "Byelorussian", "Belarusan", "Belorussian", "Balarusian". The word "Byelorussian" is an adjective derived from the transliteration of the Russian name of the country (Byelorussia). It was in predominant use in English language earlier. The adjectives "Belarusian" and "Belarusan" and many other forms emerged in the 1990s by English-speaking people to denote something or somebody of or pertaining to present-day name of Belarus, its people and the language they speak, whereas in Russian and Belarusian no new forms of the adjective appeared in those days. Both "Belarusian" and "Byelorussian" are in most common use today.
The modern Belarusian language has evolved considerably from its early roots, as the dialects of Ruthenian (East Slavic Orthodox) spoken in the territory of the Grand Duchy of Lithuania. A standardized version of Ruthenian became the official language of the Grand Duchy of Lithuania and was official language until 1696. The Belarusian was actually the language of the first printed Bible in Slavic languages, the achievement of Francysk Skaryna. The following century was Belarusian golden age: there were active many schools, religious quarell between Orthodox, Catholics and Protestants and Jews were fought using printing press rather then violence. Many Belarusians were people of Renaissance, educated at the univeristies of Western Europe or Lithuanian university in Vilnius, opened in 1570.
As a result of the so called Deluge: first Cossac wars, later Muscovy invasion and consecutive wars 1648-1667, the Belarusian population was halved, partly due to deaths, partly to the policy of deportations of the skilled cratftsman and workforce to Russia, committed by occupying Russian army. In the process schools were closed, and remaining educated people were attracted by Polish culture. By the 1696 upper classes of society switched to Polish, that was followed by the change of official language. Belarussian was used by peasants and by nobles, that wanted to express their sympathy toward crude people.
The movement of return to Belarusian was important in the circle of friends of Adam Mickiewicz.
By the 16th century, the term "Ruthenian" referred to the language spoken in modern-day Ukraine and Belarus; a process of divergence that accelerated in the 17th century created a new division between the languages spoken in the south (Ukraine) and north (Belarus) of Ruthenian-speaking territory.
Like Ukraine, Belarus and the Belarusian language has been subject to heavy Russification. Unlike Ukraine, Belarus has historically lacked a strongly nationalistic population, which tends to identify itself as a close associate of Russia (if not Russian outright). This lack of a strong ethnolinguistic identity, along with the popular association of Belarusian dialects as rural peasant languages as opposed to Russian's modern/urban connotations, is seen by some to threaten the eventual extinction of the Belarusian language in Belarus. The Russophile foreign policy of Aleksandr Lukashenko's government in Belarus is seen as further threatening the Belarusian language.
Addition: The Belarusian language is written not only in the Cyrillic alphabet (with several unique letters), but also in Lacinka (Latin script) and Arabica (Arabic script). Nowadays, the Arabic script is no longer used, but many people continue to write in Lacinka, although officially only the Cyrillic script is supported. More articles here.