Jagged, Uneven Edges? Blame Aliasing!
First and foremost, we need to understand what aliasing is. Aliasing refers to the process of sampling something in the smoothest and most continuous way possible. Programs like Photoshop do this by using a series of discrete measurements. However, if these measurements are anything less than accurate, artifacts will appear on the image. Aliasing is the reason you occasionally see misaligned pixels that didn't appear on your original image when you are saving.
An easier way to think about this is to go with a concrete example, such as follows: When dealing with objects that run horizontal and vertically, you don't have to worry about unwanted artifacts showing up. That is because these use very simple and complete measurements to showcase these. Here are some aliased shapes that still have a crisp, clean look to them.
When you begin to use shapes with curves and diagonal lines, most drawing and image editing software will begin to create unwanted artifacts within your images. These are those strange, unwanted, and unevenly jagged edges you find. Why do we get the jagged edges? Well, take a look at the limitations of your computer screen! Pixels on your screen are laid out in a grid fashion, and because you cannot create half-pixels, your screen is forced to fill in the occasional pixels here and there where you would have a half pixel. Here's an example of aliased shapes that contain jagged, uneven edges. You're going to want to click to see the full-sized image for this one!
As you can see by the two examples, a curve is actually not perfectly created on a computer, but is sort of faked by creating a gradual curve that falls along the pixel grid. Even at a distance, though, it's still noticeable that this isn't a perfect shape.