One of the main reasons Jacobus Arminius split with Calvinism was his opposition to the doctrine of supralapsarianism taught by his colleagues at Leiden University.
What is supralapsarianism? Is it a commonly held belief among Calvinists?
This word is clearly defined here.
Basically Supralapsarianism is a big word meaning 'before' 'fall' i.e before the fall. Calvin was what many call today extreme Calvinists or 'High Calvinism'. It refers to those people who believe God chose who will be saved and who damned, sealing their fate, before Adam sinned. Low Calvinists just hold predestination of those going to heaven as something God did after the fall.
Calvin and Arminian are not the only cards on the table:
He [Martin Luther] spoke at length about the idle people who occupy themselves with disputation about predestination beyond the limits of Scripture. It is most ungodly and dangerous business to abandon the certain and revealed will of God in order to search into the hidden mysteries of God. (Luther's Works Vol 54, P249)
Possibly if Calvin paid more attention to Luther's maturity on the subject of predestination Arminius would have been a Calvinist? Many of us are 90% Calvinists and 10% Arminian, but neither extreme likes us very much.
The different lapsarian views are philosophical explanations of the logical ordering of the meta-narrative of Scripture.
The chronological order is pretty clear: Creation -> Fall -> Redempetion -> Glorification
And scripture makes it pretty clear that this was the plan since "before the foundation of world" (e.g. 1 Peter 1:18-21, Revelation 13:8), so, the question that these views seeks to answer is the logical precedence.
Supralapsarians will say that the plan for redemption and election superceded the plan for the fall, because his redeemed people nec. need to be redeemed from something
On the other hand, Infralapsarians will say that the the plan for the fall came first, and from the fallen race of men came the plan for redemption and election.