Adobe Illustrator constructs objects with vector mathematics. However, it has to interpret that vector data into pixels in order to display it on the (pixel-based) monitor.
To create smooth lines on screen it anti-aliases pixels when two colors lie next to each other. It essentially “blends” the two colors together over a pixel or two in order to represent their position.
Sometimes this anti-aliasing isn’t entirely smooth if your monitor is not capable of high quality rendering. Therefore you get a small, off-color, hairline, edge with some objects.
This hairline will generally disappear if you uncheck Anti-Alias Artwork in the preferences. It will also disappear if you print the artwork or export artwork using the “Art Optimized” anti-alias setting.
This small anti-aliasing pixel is generally nothing to be concerned about.