The lac repressor is a four-part protein, a tetramer, with identical subunits.  Each subunit contains a helix-turn-helix (HTH) motif capable of binding to DNA.  The operator site where repressor binds is a DNA sequence with inverted repeat symmetry.  The two DNA half-sites of the operator together bind to two of the subunits of the repressor.  Although the other two subunits of repressor are not doing anything in this model, this property was not understood for many years.
Eventually it was discovered that two additional operators are involved in lac regulation.  One (O) lies about −90 bp upstream of O in the end of the lacI gene, and the other (O) is about +410 bp downstream of O in the early part of lacZ.  These two sites were not found in the early work because they have redundant functions and individual mutations do not affect repression very much.  Single mutations to either O or O have only 2 to 3-fold effects. However, their importance is demonstrated by the fact that a double mutant defective in both O and O is dramatically de-repressed (by about 70-fold).
In the current model, lac repressor is bound simultaneously to both the main operator O and to either O or O.  The intervening DNA loops out from the complex.  The redundant nature of the two minor operators suggests that it is not a specific looped complex that is important. One idea is that the system works through tethering; if bound repressor releases from O momentarily, binding to a minor operator keeps it in the vicinity, so that it may rebind quickly. This would increase the affinity of repressor for O.