Pie Crust -- Cutting to mix
This Serious Eats article explains it very clearly:

First he presents the "old school" understanding of what is happening:


  Old school pastry books will tell you that when you cut butter or some other solid fat (like shortening or lard) into flour, what's happening is that you are encasing pockets of flour inside a shell of fat. Add water, and the flour is moistened, whereupon gluten—the network of proteins that lend structure to baked goods—is formed. When you subsequently roll this dough out, these pockets of fat stretch and stretch, eventually forming sheet of fat that separate sheets of gluten-enforced flour. Then, as the pastry bakes, the fatty layers melt, allowing the floury layers to separate from each other, solidify, and form the layers you see in a great pie crust.


Then he points out that this doesn't really make sense:


  For starters, how could the action of cutting a solid fat into a relatively fluid mass of flour possibly cause it to coat pockets of flour in distinct bubbles? And even more importantly, if the fat is really coating these pockets of dry flour, then how would they get moist when you add water to the mix? Wouldn't the fat prevent any water from reaching the flour?


Then he states his understanding of what's actually happening:


  You see, it turns out that when it comes to pie dough, our existing model has it wrong. In fact, it's not the fat that's coating pockets of dry flour. It's the reverse. It's the flour that's coating pockets of pure fat. With this model, things make much more sense. You can easily and intuitively see how fat gets coated with flour (think about dropping a pat of butter into a pile of flour, but on a much smaller scale), and with this model, when you add water, you are indeed moistening dry flour so that it can form sheets of gluten.


From there, he goes on to present his method for getting great pie crusts by over-saturating the flour and then adding more flour to bring it back to the correct consistency.