Since the above user already posted a link to the definitions, I'll take up the reason for the debate. Bear in mind, the great divines of Reformed orthodoxy were not agreed up on these things, and both were present at Westminster. The confessions do not exclude the possibility of either view. This is a logical debate only.

The reasons why many (actually, most) have been reluctant to hold a supralapsarian view are the following:
1.) It seems to state that God reprobates creature before they have actually sinned. Most avoid this issue by stating that God elected his people before the fall, but only pretermitted the rest; then, upon sin entering, those who were passed over in the decree of election are reprobated.
2.) It has the potential of subordinating Christ to the decree of predestination. In decreeing the elect to glory, then upon occasion of the fall it was necessary in keeping with this decree to reconcile them to God, and the only method by which this could be done is the God-man, Jesus Christ. Thus God acts, not freely, but by constraint.
3.) Many have attempted to assert that this view assigns to God a much more awful role in the fall of man (which, however, is what non "Calvinists" charge against "Calvinists," as well...)
4. Infralapsarianism, according to its proponents, is much more faithful to the plan of scripture--creation, fall, setting apart a people.

The supralapsarianists claim the following against infralapsarianism:
1.) It is simply not logically consistent enough, and has the potential of making the decree of God dependent upon man. God does not receive as much glory.
2.) Many biblical passages, such as Romans 9 where Paul speaks of God as having the right to form the clay however he should desire. God is not simply restoring deformed pots, but is creating pots either for goodness or for destruction.

There are obviously many more objections against both, and, of course, actual reasons for adhering to both. These are simply some of the causes of debate, as you have asked for.

For explanation of a supralapsarian position, I would highly recommend Thomas Goodwin's treatise on election (it's long, though, so you may simply wish to jump to the book on the order of the decree); also, Perkins and John Gill. For a classic defense of the infralapsarian position, I could not recommend Turretin's treatment enough in his Institutes of Elenctic Theology.

Also, be careful: both sides will always claim Calvin for themselves.

Ultimately, the vast majority of the reformed tradition has been infralapsarian, but the supras always put up a good fight and raise many points which cannot be ignored.

Hope this helps a little.

__________________
Paul Korte
OPC
Flint, MI

They who perceive in themselves discoveries of the divine goodness, so full and absolutely perfect, and who make them the subject of earnest meditation, will never embrace new doctrines, by which the very grace they feel so powerfully in themselves is thrown into the shade. --John Calvin

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