Cake flour contains less protein than all-purpose flour and forms weaker gluten, which means it will produce a more tender product. It has also undergone a special bleaching process (distinct from the process used for other white flours) that increases the flour's ability to hold water and sugar. When used in baked goods with a high ratio of sugar to flour, cake flour is better able to hold its rise and less liable to collapse. As the name suggests, it's the preferred flour for many kinds of cakes, as well as biscuits, and some pastries and cookies.
3-3/4 oz. cake flour = 1 scant cup
If you can't get cake flour, in many cases you can substitute all-purpose, especially one with a low protein content (such as White Lily), but your results won't be exactly the same. For instance, cakes baked with all-purpose flour will be denser and won't rise as high. For every cup of all-purpose used in place of cake flour, take away 2 Tbs. of the total amount of flour used.
For most accurate measuring, use a scale. To measure by volume, fluff the flour with a fork, then spoon the flour from the bag into a dry measuring cup and level it with a knife. Never scoop right form the bag, which would compact too much flour into the measuring cup. Don't shake or tap the cup, as this packs down the flour, too.
Store flour in an airtight container in a cool, dry place away from direct sunlight.