Viewed from a high-level perspective, as meat is heated the components that make it up change. These changes result in structural transformations that affect the texture, juiciness, and mouthfeel of the meat. The higher the temperature of the heat applied to the meat, the faster these changes happen.
Here is a more detailed look at the process.
Raw meat is generally squishy, chewy, and full of moisture.
At 120°F (48.9°C) meat slowly begins to tenderize as the protein myosin begins to coagulate and the connective tissue in the meat begins to break down. This also causes the meat to firm up as the protein contracts. As the temperature increases so does the speed of tenderization.
Below about 140°F (60°C) the meat is tenderizing much more quickly than it is contracting, resulting in minimal moisture loss. Holding meat at a lower temperature means that you can tenderize the meat without losing much moisture. The meat will taste like a tender piece of medium rare meat.
However, that 140°F (60°C) temperature is a type of tipping point, above which the protein contraction greatly speeds up. A piece of meat cooked for 48 hours at 141°F (60.5°C) will be much drier than one cooked at 139°F (59°C), even though they are only 2° apart. At this point, the proteins begin to visually clump.
There are similar tipping points at 150°F (65.6°C), where the meat dries out even faster, and at 160°F (71.1°C), above which meat becomes completely dried out.
However, above 160°F (71.1°C) collagen also begins to break down very rapidly. So while the the proteins are contracting together and squeezing out the moisture, the collagen is breaking down, releasing flavorful and lubicating gelatin, and separating the protein clumps. The results in the typical pulled pork or shredded beef texture of protein clumps that can be easily separated into strands.
With sous vide you can precisely hold a temperature so you can determine the exact texture you want your final dish to be.
Most of this content came from my bestselling book, Modernist Cooking Made Easy: Sous Vide. For a really good look at this process, as well as many other scientific underpinnings of cooking, I highly recommend On Food and Cooking by Harold McGee.