The American Standard Version (ASV) of 1901 was a thorough American revision of the English Revised Version (ERV) completed in 1885. The distinctive feature of the ERV was that it was the first English Bible to use a Greek text based on the codices that had come to the attention of scholars since 1611 - Alexandrinus in the 1600s and Vaticanus in the 1800s.
One of the publications from the ERV committee states:
The Greek text followed by these Revisers is of far higher authority than that known and followed by the King James' revisers. Their Greek text was based on manuscripts of the later parts of the Mediaeval Ages, but ours has been Perfected by the discovery of far more ancient manuscripts, and by an abundance of quotations from the early fathers of the Church, and use of ancient versions. (Source)The version is literal in translation approach, very similar to the KJV. In fact, part of their object was to remain as similar to the KJV as possible - revealing the strong influence that translation had on religious life for the English-speaking world even 250 years later. The chairman of the American Revision Committee is reported to have said: "The revision will so nearly resemble the present version, that the mass of readers and hearers will scarcely perceive the difference[.]" (Source)
The same publication quoted above in reference to the ERV states their approach explicitly:
Of the handful of readings I reviewed in the ASV, it seemed substantially similar to the KJV - even keeping "thee", "thou" and "thy." The one idiosyncratic thing I noticed was the substitution of "Jehovah" for the divine name instead of "LORD." They note their particular decision to translate that way in the preface to the ASV:
From the outset the object sought by the revisers has been "to adapt King James' version to the present state of the English language without changing the idiom and vocabulary,'' and further, to adapt it to "the present standard of Biblical scholarship." Since 1611 this latter has made great advances, especially during the last quarter century.
One of the Committee stated his understanding of the object sought in these words: "The new Bible is to read like the old, and the sacred associations connected with it are not to be disturbed; but within these limits all necessary and desirable corrections and improvements on which the best scholars are agreed will be introduced: a good version will be made better; a clear and accurate version clearer and more accurate; the oldest and purest text is to be followed; errors, obscurities and inconsistencies are to be removed; uniformity in rendering Hebrew and Greek words and proper names to be sought. In one word, the revision is to give, in idiomatic English, the nearest possible equivalent for the original Word of God as it came from the inspired organs of the Holy Spirit. It aims to be the best version possible in the nineteenth century, as King James' version was the best which could be made in the seventeenth century." (Source)
The change first recommended in the Appendix - that which substitutes "Jehovah" for "LORD" and "GOD" - is one which will be unwelcome to many, because of the frequency and familiarity of the terms displaced. But the American Revisers, after a careful consideration were brought to the unanimous conviction that a Jewish superstition, which regarded the Divine Name as too sacred to be uttered, ought no longer to dominate in the English or any other version of the Old Testament, as
it fortunately does not in the numerous versions made by modern missionaries.
The change was not followed by the main subsequent English versions, and it is now known that "Jehovah" was never the proper pronunciation for the divine name anyway (being the vowels of one word written with the consonants of another).
The version is still important as the first American translation to incorporate the results of biblical scholarship, especially related to the New Testament text. All but a few English versions now use Greek texts based on those same earlier manuscripts. It's also important as the starting point for many of the more formal-equivalent translations used today. The RSV, NRSV, ESV, and NASB are all related to the ASV.
To get a taste for the ASV as a translation, here's Psalm 23.
1 Jehovah is my shepherd; I shall not want.
2 He maketh me to lie down in green pastures; He leadeth me beside still waters.
3 He restoreth my soul: He guideth me in the paths of righteousness for his name's sake.
4 Yea, thou I walk through the valley of the shadow of death, I will fear no evil; for thou art with me; Thy rod and thy staff, they comfort me.
5 Thou preparest a table before me in the presence of mine enemies: Thou hast anointed my head with oil; My cup runneth over.
6 Surely goodness and lovingkindness shall follow me all the days of my life; And I shall dwell in the house of Jehovah for ever.
If you're interested in the history of English Bible translations, I've found Michael Marlowe's Bible Research website to be an excellent source of information. The translators' preface and many other relevant primary documents can be found there.
All in all, the ASV is a solid, literal translation of the Bible. The language is a bit archaic, even for the late 19th century, but I suppose that was necessary to retain the flavor of the KJV as much as possible.