Most of the structures in the Protein Databank are determined with X-ray crystallography. Like inorganic compounds and small organic molecules, under the right conditions proteins can form crystals - ordered, repeating patterns of protein molecules, filling a 3D space. That is, you can take a basic building block and rotate and translate this building block to completely fill the three-dimensional space. (2D example).
So what's being modeled in an X-ray crystallography experiment is that basic building block, the one which undergoes symmetry operations (rotation and translation) in order to fill out 3D space. This basic building block is called the asymmetric unit, because it is without the crystallographic symmetries which result in filling space.
But even in the asymmetric unit there can exist noncrystallographic symmetry. These are symmetries (rotations and translations) which relate portions of the asymmetric unit, but aren't lined up quite right to fill space. Because they don't contribute to the overall symmetry of the crystal, normally they're not exactly symmetrical. Usually there are slight differences, based on how the noncrystallographic symmetry fits into the crystallographic one.
For a 2D example, think of a triangle which is tiled on a square grid. The square grid is the crystallographic symmetry. The triangle has noncrystallographic symmetry, because the three-fold rotational axis of the triangle does not contribute to tiling the plane. This means the corners of the triangle are not exactly equivalent, as each corner is in a different position with respect to the neighbors in the next square.
So when an X-ray cryptographer goes to solve the structure of a protein crystal, the primary unit of interest is the asymmetric unit - even if there's noncrystallographic symmetry in the asymmetric unit. So that's what the PDB records as its primary entry - the contents of the asymmetric unit, including the slight differences between any repeated units.
In your case (1iep), that's what happened. Because of the specific way the protein crystallized, there just happens to be two copies of the protein in the asymmetric unit, almost - but not quite - identical to each other. This representation of the asymmetric unit - including both proteins - is what you've downloaded.
Because this might not be what you're interested in, the PDB also provides one or more "Biological Assembly" files. These are processed files which attempt to model what the experimentalists believe* is the actual biologically relevant unit. In your case, the relevant biological unit is a monomer, so they provide two biological assembly files - one for each (distinct) monomer in the asymmetric unit. For multimeric proteins, it sometimes happens that one of the symmetry axes for the multimer lines up with the crystallographic axis. In this case, you'd only get part of the protein in the asymmetric unit download, but the biological assembly file would contain a reconstructed representation of the multimer.
If you want further, extensive detail, I would second the recommendation made here to look at the textbook Crystallography Made Crystal Clear, by Gale Rhodes.
(*The biological unit provided by the PDB is a guess. Sometimes you'll see proteins which should be multimeric represented as monomers, or monomeric proteins represented as multimers. It depends in part on how accurately the depositors annotated what the relevant biological unit was.)