Can you explain this Free Will / Predestination illustration? I've heard multiple preachers explain Free Will and Predestination with this illustration:


  Free Will and Predestination are like a door. The side of the door toward us says, "Free Will." Once you go through the door you turn around and see that the other side says, "Predestination."


Could someone that understands what this illustration means explain it to me?
The point of the illustration is to reconcile God's sovereignty in salvation with man's free will to choose salvation.  I believe it originated from H.A. Ironside:


  It has been pictured in this way. Here is a vast host of people hurrying down the broad road with their
  minds fixed upon their sins, and one stands calling attention to yonder door, the entrance into the
  narrow way that leads to life eternal. On it is plainly depicted the text, "Whosoever will, let him
  come." Every man is invited, no one need hesitate. Some may say, "Well, I may not be of the elect,
  and so it would be useless for me to endeavor to come, for the door will not open for me." But God's
  invitation is absolutely sincere; it is addressed to every man, "Whosoever will, let him take of the
  water of life freely" (Rev. 22: 17). If men refuse to come, if they pursue their own godless way down
  to the pit, whom can they blame but themselves for their eternal judgment? The messenger
  addressed himself to all, the call came to all, the door could be entered by all, but many refused to
  come and perished in their sins. Such men can never blame God for their eternal destruction. The
  door was open, the invitation was given, they refused, and He says to them sorrowfully, "Ye will not
  come unto Me, that ye might have life." ... [But some will say], "I am going inside: I will accept the invitation;
  I will enter that door," and he presses his way in and it shuts behind him. As he turns about he finds written on the inside of the door the words, "Chosen in Christ before the foundation of the
  world.  
  
  H.A. Ironside, In the Heavenlies (Ephesians), pages 27-28


The illustration distinguishes the cause of salvation into two perspectives: the perspective of man, and the perspective of God.  The idea is that from our perspective, we use our "free will" to choose to be saved.  And from God's perspective, God uses his sovereignty to choose who will choose salvation.

The point of the illustration is to defend against the the objection to Calvanism that if predestination is true, then not everyone who wants to be saved can be saved.  This illustration counters this by arguing that everyone who wants to be saved can - because everyone who wants to be saved was predestined to be saved.  It attempts to reconcile the notion that anyone who wills to be saved can be saved, with the notion that God chooses who will be saved.