It is said that the dip in the middle of the four sides of the Khufu pyramid, or the ‘hollowing’ as Petrie puts it, was first noticed in an aerial photograph taken in the 1940′s by a British Airforce pilot flying
over the Giza plateau.

As far as I am aware few explanations exist on this and none are conclusive. It’s another one of the pyramid’s mysteries. Petrie discusses it in chapter 6 of his
The Pyramids and Temples of Gizeh. As to why this feature might have been used he writes:

The object of such an extra thickness down the midline of each face might be to put a specially fine line of casing, carefully adjusted to the required angle on each side; and then afterwards setting all the remainder by reference to that line and the base.

Larry Orcutt has an informative page on the topic also.