The stance in Aikido is called hanmi (半身). Hanmi translates as "half body" as you can see from the picture. The type of hanmi depends on the style of Aikido one studies. The shoulders and hips can be square or one can be drawn back. This limits the amount of exposure to your vital areas. Generally speaking, the front foot is straight while the back foot is either straight or turned out, but again it depends on the style of Aikido or martial arts one does. The front knee is almost always bent and the back leg is almost always straight.
The stance in Aikido has a two fold rationale. First, the stance is the foundation by which power and movement are generated. How one stands and how the hips and feet are placed generally indicate how movement and thus power will be generated. Secondly, the stance is the basis for one's defense. In the past, the stance was used to hide the vital areas which housed major blood vessels, organs or weak spots.
Just about every teacher of Japanese traditional art's can be heard rebuking their students with, "Do it from the lower body." The stance is said to be an expression of one's experience level. Beginners traditionally take a more closed stance which enables them to "hide" their openings while masters tend to take a more open stance "creating" their openings. Thus, we can see why the stance is considered the "foundation" of the art.