Dispensationalism is a theological belief system devised by J. N. Darby (founder of the Exclusive Brethren) that divides human time into different ages, called dispensations. It aims to show how God's plans and purposes have changed throughout history not gradually but in large steps.
Each dispensation is a period during which God works in a specific way. There is a change of dispensation when God gives humanity a different revelation of his will to follow.
Another way of looking at it is to consider a dispensation as a period of government. Different governments bring different ways of running a country - in different dispensations the same God runs the world in a different way.
C. I. Scofield, editor of the Scofield Reference Bible, devised the most commonly used dispensational breakdown of human history. He listed seven dispensations:
Innocence - from the beginning to the fall
Conscience - from the fall to Noah
Human Government - Noah to Abraham
Promise - Abraham to Moses
Law - Moses to Christ
Church - the present age
Kingdom - beginning at the Second Coming of Christ
Scofield wrote about the change from dispensation 5 to dispensation 6:
As a dispensation, grace begins with the death and resurrection of Christ...The point of testing is no longer legal obedience as the condition of salvation, but acceptance or rejection of Christ, with good works as a fruit of salvation.
So in the present dispensation God tests us by seeing if we reject or accept Christ. In the previous dispensation God tested us by seeing if we obeyed the law.
For those who accept it, dispensationalism provides a way of interpreting the Bible literally and consistently without contradictions.
Dispensationalists say that in each dispensation God is using different revelations and so the Bible only has to be consistent within a particular dispensation.
So contradictions in the Bible are only contradictions on the surface. If studied properly they turn out not to be contradictions at all, because different rules operate within each dispensation.
Critics say that the idea of dispensationalism is something that Darby made up himself ("concocted in complete contradiction to all main Christian traditions", said James Barr), but Darby believed that the idea had been given to him by God.
Dispensationalism wasn't a brand new doctrine anyway; Joachim of Fiore had put a similar idea forward in the 12th century CE.
In this version of dispensationalism the dispensations are not rigidly separated at an instant in time but gradually progress from one to another. In each dispensation it's possible to find early signs of the dispensation to come.
Progressive dispensationalists interpret the Bible in a less literal way than other dispensationalists.
Postmillennialists believe that the Second Coming of Christ will come at the end of the Millennium and mark the full achievement of the kingdom of God on earth.
They believe that we are already in the Millennium, which began with Christ's resurrection, and that the world is gradually moving towards the promised time of peace and righteousness. Christ is ruling earth from heaven, through his church and through believers, and his kingdom and rule are steadily growing.
This view can lead to either of these two possible practical consequences:
The church should take a major social and political role in reshaping the world to advance God's Kingdom on earth
Countries should be ruled by theocracies (religious governments) as this is the way to bring about God's Kingdom
Amillennialists don't believe in the Millennium as a specific period of 1000 years, and regard Biblical reference to it as symbolic.
They believe that the millennium began when Christ was born on earth and will end with the second coming. Amillennialists say that Christ is reigning now, both in heaven, and on the earth in the hearts of believers.
The doctrine, which was made popular by St Augustine, is accepted by the Roman Catholic church and many middle of the road Protestant denominations.