It's easy to mix honey and water together; the real challenge in mead making is keeping your yeast healthy and happy. Stirring and aerating are both important parts of the mead making process that will help keep your yeast going and make a great tasting final product.
During the first stages of fermentation, the yeast uses oxygen to reproduce. When oxygen is present the yeast cells do not produce much alcohol, but rather use the available oxygen to engage in cell division. This creates rapid growth of the yeast colony, which is beneficial to the fermentation. Supplying your must with a lot of oxygen can greatly aid the fermentation and avoid unpleasant off-flavors caused by yeast stress. Many mead makers will vigorously stir or splash their must to work oxygen into it prior to fermentation. Using a mix-stir or wine whip makes this a lot easier and less time-consuming. An aeration system that injects air or pure oxygen (Oxygenation Kit 2.0) through a diffusion stone is even easier to use.
Some mead makers will continue to supply oxygen to the mead through the first few days of fermentation in order to increase the yeast culture size even more. This practice is fine up until the point at which 1/3 of the sugars have been consumed. After this point, the oxygen could contribute to oxidative staling, and should be avoided. Stirring after fermentation has begun has the added benefits of mixing the solution and removing co2 from the solution. Be sure to start stirring slowly, otherwise, the rising co2 can cause excessive foaming.