Why is the order of The Chronicles of Narnia changed from original publication?

The question of reading order for The Chronicles of Narnia is a complicated one, with much debate even among avid fans of the series. But you've asked only why publishers changed the order, which is much easier to answer objectively than which order is "best"/preferable.

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The answer lies in a letter which Lewis wrote, dated April 1957, to a young American fan named Laurence Kreig. The boy preferred internal chronological order (starting with The Magician's Nephew) while his mother preferred publication order (starting with The Lion, the Witch, and the Wardrobe). Lewis said:

I think I agree with your order for reading the books more than with your mother's. The series was not planned beforehand as she thinks. When I wrote The Lion I did not know I was going to write any more. Then I wrote P. Caspian as a sequel and still didn't think there would be any more, and when I had done The Voyage I felt quite sure it would be the last, but I found I was wrong. So perhaps it does not matter very much in which order anyone read them. I’m not even sure that all the others were written in the same order in which they were published. I never keep notes of that sort of thing and never remember dates.

In C.S. Lewis's Collected Letters, Volume 3, pp. 847-8, the following footnote is added to this letter:

In the summer of 1963 Lewis had Walter Hooper write down the order in which he preferred the stories to be read: The Magician’s Nephew; The Lion, the Witch and the Wardrobe; The Horse and His Boy; Prince Caspian; The Voyage of the ‘Dawn Treader’; The Silver Chair; and The Last Battle. Regarding the order in which the stories were written, see CG, ‘The Writing of the Narnias’, pp. 401–5.

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The US publication rights were originally owned by Macmillan, who preferred the original publication order starting with The Lion, the Witch, and the Wardrobe. In 1994, Harper Collins took over the US publication rights, and they changed the order to internal chronological order starting with The Magician's Nephew. Why? In the 2005 Harper Collins editions, the publishers added the following note:

Although The Magician's Nephew was written several years after C. S. Lewis first began The Chronicles of Narnia, he wanted it to be read as the first book in the series. HarperCollins is happy to present these books in the order in which Professor Lewis preferred.

TL;DR: Lewis himself expressed a preference for internal chronological order, at least a couple of times, and the publishers of later editions decided to follow this.

_{Further reading: Paul Ford, Companion to Narnia: A Complete Guide to the Magical World of C.S. Lewis's The Chronicles of Narnia, 2005. Hat-tip also to Wikipedia and Jon Ericson's blog and comments for guiding me to some useful sources.}