The issue is a division over the order of the decrees. Supralapsarians place election in the mind of God before the fall into sin. That is, from Latin, "supra," above, "lapsus", the fall. Infralapsarians (also called "sublapsarians"), in contrast, place the fall ahead of election. That is, "infra," below, "lapsus," the fall. The difference is over whether God elected a people, then used the creation and fall of Adam to attain the goals of election. Or did He create Adam, who then fell, and then God elected a people as a remedy for the fall. Note that these are not intended to be considered actions in time, but rather the purposes in the mind of God.
To my mind, supralapsarianism reserves election to the issue of God's glory, alone. God is glorified when His attributes are exhibited. Accordingly, election served to satisfy God's existence, not man's. For example, Paul explains that predestination reveals the glory of His mercy (Romans 9:23), of His grace (Ephesians 1:6), and of His riches (Ephesians 1:18). While predestination certainly occurred in love (Ephesians 1:4-5), even that was first His love to us, not ours to Him (I John 4:19, but also in the entire passage of verses 7-21). In other words, to glorify His attribute of love.
In addition, it seems to me that only the supralapsarian view gives full credence to Romans 9:21: "Has the potter no right over the clay, to make out of the same lump one vessel to honorable use and another for dishonorable use?" That certainly seems to place God's will as the a priori principle of predestination and reprobation, not a posteriori as required by infralapsarianism.
While both supralapsarians and infralapsarians place the decrees in the mind of God before the Creation, i.e., before time (see Ephesians 1:4, Hebrews 4:3, and Revelation 17:8), infralapsarians still view election as a remedy for the fall. Their reasoning is that to do otherwise makes God the author of sin. And I certainly grant that as a serious issue. However, I suggest that the objection must be made to Paul, not to supralapsarians. I don't know how to resolve this particular question. However, since I consider all of Scripture to be the Word of God, I must submit to what the Scripture says, and let my own doubts or questions fall wherever they may. And the question is, indeed, acknowledged even in the Scriptures themselves. In Isaiah 45:7, God says, "I form light and create darkness; I make well-being and create calamity; I am the Lord, Who does all these things."
And finally, I have a problem with the idea of God's doing something to remedy an action of man, as if He were caught by surprise. That makes the purposes of God subject to men, while Scripture puts men subject to the purposes of God (Isaiah 42:8, 43:7, and 48:11).
The first question of the Westminster Shorter Catechism correctly states that the chief end of man is "to glorify God and enjoy Him forever." However, fallen man turns it around and acts as if God's chief end is to glorify man! Reformed theology is a correction to that crowning error of humanism. And supralapsarianism seems to me to be the consistent application of Reformed, i.e., biblical, theology.
Addendum on 12/1/13: I am reading the Reformed Dogmatics of Dutch-American theologian Herman Hoeksema. His answer to the question of God as author of sin seems reasonable. He says that sin lies in the motivation, not in the act per se. He gives the example of killing. Murder for gain is sinful; the execution of a criminal as an act of justice is not. Therefore, God's purpose in predestining the acts of the reprobate contains no sin, because His purpose is to further His plan of redemption of the elect. The act may be sin in the person committing it, because his motivation in the act is sinful, but that motivation is the responsibility of the sinner, not of the providence of God.