This excerpt is taken from John Sanders' book, The God Who Risks:
"After my conversion some Christians informed me that my brother's death was ordained for the purpose of bringing me to faith in Christ. What? God killed my non-Christian brother so that I would become a Christian? But without middle knowledge God could not have known that this would happen. This would mean that God kills people and causes disasters in the hope that some may repent and confess Christ. However, the model of general sovereignty does not allow for each and every such evil to be explained this way, since God is only responsible for the structures within which we operate and for those specific acts in history God elects to do" (page 262).
Sanders explains "middle knowledge" on pp. 196-198 of his study. In short, middle knowledge (in this context) has reference to the divine awareness of all "counterfactuals of creaturely freedom" which means that, according to this theory, God knows what would happen in the world He chose to create if X, Y, or Z respectively obtained (let X, Y, and Z = possible worlds or counterfactual situations). Sanders illustrates this somewhat abstruse notion with a fitting concrete example about asking a child to do some necessary chore around the house.
If anyone here has ever asked a son or daughter to take out the trash or wash the car, he/she can pretty much understand how different conditions (X, Y, Z) influence a child's willingness to do A (i.e. a certain specified action). Furthermore, most of us are aware of the fact that if S (a particular rational subject or moral agent) had been raised in a developed country instead of a developing land, then he/she might have performed A instead of ~A. But we could not infallibly guarantee that A would be performed instead of ~A. Nonetheless, the "counterfactuals of creaturely freedom" notion indicates that if S were in possible world (counterfactual situation) X, then God would know what S would do.
Hope that helps you understand what Sanders means by "middle knowledge."