Pastry flour has a lower protein content than the average all-purpose flour, making it more suitable for producing a tender dough, such as pie crust. Regarding protein content, pastry flour occupies the middle ground between all-purpose flour and cake flour. The amount of protein in flour varies by brand, region, and harvest. Generally, all-purpose flour averages about 10-12g of protein per cup, pastry flour has about 8-10g, and cake flour 7-8g. The amount of protein in the flour affects gluten formation, thus lower-protein flours make much softer, weaker dough than high-protein flour. (Bleaching also affects gluten formation, making gluten strands a bit weaker, but doesn't affect protein content.)
Pastry flour will produce a much more delicate dough than all-purpose flour. This property makes it useful if you're prone to overworking your dough or if you're using a food processor, rather than manual tools, to make dough. However, if you're trying to make a lattice-top pie crust, for instance, you should stick to all-purpose flour, as the pastry dough will most likely fall apart as you assemble the crust, unless you're an especially skillful baker. Pastry flour is also great for making all-butter pie crust, which I find enormously difficult to make well with all-purpose flour.
Commercial pastry flours are available, but sometimes hard to find or unsatisfactory. To make your own, mix two parts all-purpose flour with one part cake flour by volume. Experiment with your recipes to see what works for you. Sometimes you might need a little more cake flour, a little less all-purpose flour or vice versa.
For more information on pastry flour and its uses in baking, see Rose Levy Beranbaum's book The Pie and Pastry Bible. For a more scientific discussion of wheat flour, gluten formation, and the like, read Harold McGee's book On Food and Cooking: The Science and Lore of the Kitchen.
NB: All references to flour in this writeup refer to wheat flour.