There are three main reasons why stirring could affect the rate of dissolution. For our initial system, let's use a beaker with, let's say, a half inch layer of sugar on the bottom and filled most of the rest of the way with fresh, room temperature water. With no stirring that layer of sugar is just going to sit on the bottom. If you look very closely at the interface between liquid and solid, you can actually see some of the sugar dissolving. There will be fluid veins of different densities and will reflect light at slightly different angles (see fluid dynamics for more information http://en.wikipedia.org/wiki/Fluid_dynamics). Left alone, diffusion alone is left to make the solution uniform and since sugar water is denser than pure water, diffusion also has to overcome gravity. Stirring increases the rate of diffusion and will increase the rate of dissolution. Another important factor is surface area. The top of a thick layer of sugar has moderate to decent access to the water that is doing the dissolving, but the bottom of that layer either does not have access to water at all or quickly becomes saturated and no further dissolution can occur. This is because the rate of diffusion in and out of the solid sugar layer will be extremely slow. Stirring drastically increases the available surface area of sugar to water. Note that the total surface area of sugar at any point in time is constant, it is the surface area that is exposed to fresh water that is important. The third thing is the type of stirring, which usually revolves around the type of vessel being used. Beakers and round bottom flasks commonly used in a chemical lab generally call for magnetic stirbars. The stirbars are simply a small, usually cylindrical piece of magnetic metal (like iron) coated in Teflon so that the stirbar is inert and does not react with your experiment. These stirbars sit at the bottom of the flask, which is placed upon a stir plate. The stir plate is simply a rotating blade with magnets on the ends, which in turn causes your stirbar to rotate and stir the fluid. Since the stirbar is sitting on the bottom, stirring against the surface of the vessel, sugar will get ground up by passing between the stirbar and the vessel's surface. When the sugar gets ground up, you increase the surface area to volume ratio of the particles, which will greatly increase the rate of dissolution (due to points one and two). Let's also think of sugar sitting at the bottom of a 2L soda bottle. The bottom of the bottle is not uniform and a stirbar would be of little value here since there is no uniform surface for it to effectively stir on. Here, a paddle attached to a shaft and connected to a motor would be useful (as would shaking). The paddle can rotate at different speeds, it can be different shapes and sizes, and each of those things affects how well mixing occurs. On small scale the blade is usually called a paddle, whereas on large scale it is called a propeller. Stirring rates using motors are generally measured in RPM, but it is important to note that at a constant RPM, the longer a propeller is, the faster the tip of the propeller is going. On industrial scale the tip of the propeller can easily exceed 100 MPH. Depending on the shape of the propeller, there can be a grinding effect similar to that of a magnetic stirbar, but in general it is minimal and shouldn't be counted upon to increase surface area to aid dissolution. There is a lot of science behind mixing that I won't get into since your question was aimed at dissolving rates instead of mixing, but I wanted to give you a taste of how involve mixing can be.