Binding of the lac repressor to the sequence of 24 base pairs in the operator prevents DNase I from attacking that region of the molecule.
When the fragments are separated by electrophoresis, those representing the lengths covered by the repressor will be missing from the autoradiogram.
The resulting gap is the "footprint".
The same sample of DNA (unprotected by the repressor) is subjected to normal DNA sequencing and the resulting ladder aligned with the footprint autoradiogram.
The exact sequence of bases in the lac operator can then be read directly because they represent the rungs of the ladder missing in the footprint.