It is a form of premillennialism and it teaches biblical history as a number of successive economies or administration. These are called dispensations, each emphasising the discontinuity of the OT covenants God made with His various people.
To understand its implications, we need to look at supersessionism. It teaches that the Christian Church has been established for the salvation of "the Jews first, and also to the Gentiles", and that there is one people of God joined in unity through Jesus Christ. And since the Jews have largely refuse to accept Jesus as the Messiah, Christians have become the "New Jews".
In contrast, dispensationalism teaches that the Christian Church is a "parenthesis" in God's dealings with the Jews, that God's continued favour of the Jews will be revealed after the Church Dispensation/Age, when Jews will be restored to their land and will accept Jesus as their Messiah.
The following individuals have been associated with dispensationalism:
- Sir Robert Anderson (1841–1918), "Anglicanized Irishman of Scottish extraction", 1863 entered the Irish Bar; Assistant Commissioner of Metropolitan Police in Scotland Yard; lay preacher and defender of the Faith; saw difference between Israel and the Church; authored 19 books on the Bible.
- Charles F. Baker (1905–1994), author (A Dispensational Theology), and founder of Grace Bible College, Grace Movement pioneer.
- James H. Brookes (1830–1897), minister, writer, and theologian. Cyrus I. Scofield was one of his students.
- John Hagee pastor Cornerstone Church , writer, and theologian. Founder of John Hagee Today tv and radio program.
- Clarence Larkin (1850–1924), author of many pamphlets and books around 1918 containing extensive graphical dispensational charts with commentary
- Jack Chick (b. 1924), controversial fundamentalist cartoonist and founder of Chick Publications.
- John Nelson Darby (1800–1882), British preacher, Plymouth Brethren co-founder, and considered by many as the "father of dispensationalism."
- Arnold Fruchtenbaum (b. 1943), writer and theologian
- Mark Hitchcock, pastor and author
- Thomas Ice, writer
- Harry A. Ironside (1876–1951), pastor of The Moody Church, Chicago, and author of more than 60 books.
- Tim LaHaye (b. 1926), minister, author of the "Left Behind" novel series, and speaker.
- Hal Lindsey (b. 1929), evangelist and author of "The Late Great Planet Earth" and other books advocating a dispensationalist and fundamentalist understanding of Christianity.
- J. Dwight Pentecost (b. 1915), writer and theologian
- Charles Caldwell Ryrie (b. 1925), Christian writer and theologian. Better known for his "Ryrie Study Bible", which is known to teach dispensationalism.
- Cyrus I. Scofield (1843–1921), minister, scholar, and theologian. Better known for his influential Scofield Reference Bible (published in 1909) that popularized dispensationalism.
- Miles J. Stanford (1914–1999), Christian author and Pauline dispensationalist.
Charles Stevens, founder of Piedmont Baptist College.
- Henry C. Thiessen, author of Lectures in Systematic Theology and taught at Dallas Theological Seminary.
- Jack Van Impe (b. 1930), televangelist known for interpreting current events in light of a dispensationalist approach to biblical prophecy.
- John F. Walvoord (1910–2002), longtime president of Dallas Theological Seminary and leading proponent of dispensationalism in the late 20th century.
- Kenneth Wuest (1893–1962), New Testament Greek (Κοινή) scholar.
Ben Witherington has a very good article on Supercessionism, Dispensationalism, and the Present Middle East Crisis-- A Christian Stand in his blog.