Who is Ostwald?
In 1896 Ostwald described this phenomenon for small molecules and here are the references, but they are in German and very old, so they are probably hard to find. So instead, I recommend you read references 3 and 4 instead.
 Ostwald, W. 1896. Lehrbruck der Allgemeinen Chemie, vol. 2, part 1. Leipzig, Germany.
 Ostwald, W. 1897. Studien uber die Bildung und Umwandlung fester Korper. Z. Phys. Chem. 22: 289.
 Ng, J.D. et al. 1996. The crystallization of biological macromolecules from precipitates: Evidence for Ostwald ripening. J. Cryst. Growth 168: 50.
 Boistelle, R and Astier, J.P. 1988. Crystallization mechanisms in solution. J Cryst. Growth 90: 14-30.
Phase diagrams, by the way, are also known as Ostwald-Mier diagrams or sometimes just Mier diagrams.
Definition of Ostwald ripening
Many small crystals form in a system initially but slowly disappear except for a few that grow larger, at the expense of the small crystals. The growth of the larger crystals is thermodynamically favored with respect to the growth of the smaller ones. To put it another way, the smaller crystals act as "nutrients" for the bigger crystals. As the larger crystals grow, the area around them is depleted of smaller crystals, giving rise to the characteristic "halo" effect around the growing crystals.
Explanation for the occurrence of Ostwald ripening
This is a spontaneous process that occurs because larger crystals are more energetically favored than smaller crystals. This might be hard to believe seeing as how it seems far more common to get many small crystals than a few large ones, but there is a believable explanation. While the formation of many small crystals is kinetically favored, (i.e. they nucleate more easily) large crystals are thermodynamically favored. Thus, from a standpoint of kinetics, it is easier to nucleate many small crystals. However, small crystals have a larger surface area to volume ratio than large crystals. Molecules on the surface are energetically less stable than the ones already well ordered and packed in the interior. (Think of packing your vacation clothes in a suitcase. Which ones are more energetic? The ones buried in the middle or the ones you are packing in on top, trying to get them to fit?) Large crystals, with their greater volume-to-surface area ratio, represent a lower energy state. Thus, many small crystals will attain a lower energy state if transformed into large crystals and this is what we see in Ostwald ripening.
For a mathematical description of this, see reference .
So why doesn't Ostwald ripening happen all the time? One reason is that the nucleation of many small crystals reduces the amount of supersaturation and thus, the thermodynamically favored large crystals never get a chance to appear.
Pictorial example of crystal ripening from a precipitate.
The pictures here show crystals growing at the expense of precipitate, which represents a phase transition. Thus, this is not an example of Ostwald ripening. Ostwald ripening is not a transition of the protein from one phase (precipitate) to another (crystal). Ostwald ripening means big crystals growing at the expense of little crystals. However, the depletion zones around the growing crystals which are seen here are also seen in Ostwald ripening and until I get some pictures of true Ostwald ripening, this is the closest example I have. Other common examples of phase transitions are from oils to crystals, or spherulites to crystals.
Day 6A single crystal has appeared in the precipitate. The precipitate feeds the growth of the crystal and a zone of depletion appears around the crystal as it grows. This depletion zone looks like a halo around the crystal.
The precipitate had completely disappeared.
Day 3, different protein
Here is different protein. This is an example of Ostwald ripening induced by streak seeding into the precipitate. Initially the protein completely precipitated in the drop (day 1). I then streak seeded through the precipitate. (Do you see the seed line in the upper right-hand quadrant?) Yes, you just draw the seeding tool (usually a cat whisker or horsetail hair) through the precipitate. The drop doesn’t have to be a clear drop to be seeded. You can seed into any supersaturated state of the protein. In this example, crystals began to grow by Ostwald ripening, first along the seed line, and then even away from the seed line.