In traditional 2D animation, being comfortable with drawing will help you in creating strong character designs, creating believable motion, conveying weight and momentum through your drawing style, understanding directional light and shadow, and maintaining consistency between frames of animation. While you don't have to be an artistic master, it still helps to hone your traditional art skills so that even if you're producing simplistic animations, you'll still be consistent in technique.
In 2D computer animation, said drawing skills may not be so critical considering how often you'll be tweening your animations. These skills are still important to character design and principles of motion, as you can't always trust the program to do it for you. Learning to draw is about more than just creating still images; it's about understanding the physics of those still images and recreating that physics believably using line, shading, and color. This can be as true of an image of a woman running as it is of an image of a leaf blowing in the breeze. Learning to draw is, in many ways, about studying motion - and motion is, of course, the key principle of animation.
In 3D computer modeling and animation, the same reasons apply, but take on even more depth. Suddenly a fine art lesson on directional light becomes the foundation for creating atmospheric lighting in a 3D scene; the theory involved in drawing motion studies lays the groundwork for creating realistic, fluid motion in your 3D models; lessons on depth and texture contribute to creating bump maps and texture maps that enhance your scene.
So in short: while you don't have to be a master of fine art to be a successful animator, learning the principles of art and drawing theory can enhance your animation skills and make you a more well-rounded animator.
