God sees all possible worlds that he could create and all the interactions between His soveriegn choices and the free-will choices of man. Out the infinite worlds He could create He freely chooses one that conforms to His will and good pleasure.
Molinism derives its name from a 16th century philosopher, Luis de Molina (1535-1600), who first put forth the view. It has recently been resurected by modern philosophers such as William Lane Craig and Alvin Plantiga. Its goal is to reconcile God's Foreknowledge and man's free will. Historically, this has been done in two ways. First, many theologians have decided to downplay or overemphasize God's soveriegnty or man's free will. Open Theism (see Presentism) is completely free-will oreinted such that God cannot accomplish His will unless humans cooperate with Him. Extreme Calvanists deny that man has a free will altogether. A second option, one that many tend toward after spending any time on the subject, is to simply appeal to God's mysterious ways. While it is legitimate for the Christian to make this appeal in some circumstances, Molinists do not believe this necessary.
The View Briefly Defined
God's knowledge of the future has three stages (or logican steps) as He decides what world He will create. His Natural Knowledge includes in infinite number of universes that God could create. In each of these worlds, every man and woman has a free will. These universe may include God completely changing the construction of life from carbon to silicon or some other substance. He may chose to interact with these various world's in whatever way He choses which may cause humans to make different choices.
Out of these worlds in His Natural Knowledge, only some may make sense according to what He may want to have happen. The next "stage" of His knowledge then is Middle Knowledge - all the possible choices humans might make. He then choses to create or actualize one of these worlds, the world we live in today. The events that He saw would happen in this world then become His Free Knowledge.
Because God's Middle Knowledge allows Him to know what every possible person would do of their own free will in every circumstance, He knows under what circumstances each person might or might not recieve Christ (according to their own free will). This allows Him consider all feasible worlds where each person's free will choices line up with His desires (Eph. 1:5, 11). In a seeming paradox, both God's soverignty and man's responsibility and free will are maintained when He chooses to actualize a particular world. His Middle Knowledge of what would happen then becomes His Free Knowledge of what will happen - what we call Foreknowledge. His Foreknowledge though, does not determine what a person must do, only what they will do according to their own free choices - in a world that God soverignly actualized! Scripturally this may be based on (Rom. 8:29) where God's Foreknowledge of what would happen precedes His predestining those who freely choose Him.
The view of election here is God's soveriegn choice of whom He will allow to freely choose Him based on the circumstance He choses to place before them. It may appear similiar to the Arminian view that predestination is God looking ahead through time to those that would choose Him and then electing those to be saved. It may also appear fundamentally the same as the Calvinist view that God chooses those that will come to salvation and chooses those that will be condemned. Ultimately, it may appear similiar to both views because it affirms the scriptural truths in each without compromising in other areas or appealing to mystery. This does not make it correct, because it is not itself an explicitly biblical teaching, but it does present a coherent, working theory of the combatibility of foreknowledge and free will.
In the Molonist view, God could have chosen a different world where different people came to know Him. This brings up many questions and Molonism provides some interesting answers. Because God desires that all come to Him (1 Tim 2:3-4), it could be argued that there was no possible world wherein all men with free choices would accept Christ, no matter how much revelation they were given (John 6:44; Rom 1:19-20; I John 4:19). The answer to the question of the pagan that hasn't heard the gospel may be answered by asserting that in even all feasible worlds, that person would never have recieved Christ. On the other hand, John 6:27 seems to say that man cannot resist if God wills his salvation. Molonism is also flexible enough to allow God to create a world where some events are completely determined by Him, but man retains free will in all other situations.
As desirable as it is to have answers to these questions, the Christian, the theologian should not overstep scripture to find them. It is this author's opinion that it presents the most coherent view, but should not be relied upon as a Biblical truth