Most movement in nature, unless it is very short, travels in an arc rather than a straight line. For example, when you are reading a book, take your hand from the page and touch your nose. Unless you are holding the book no more than a few inches from your face, your hand will trace an arc in the air. When animating, an absence of arcs will result in very stiff, abrupt, and unnatural movement.
To get a clear example of arcs, take a look at the amazing photography of Harold Eugene “Doc” Edgerton (1903 – 1990), who specialised in the use of high-speed stroboscopic photography.
The photography techniques he developed allowed him to record an action at far greater speeds than what was possible with a mechanical camera.
Have a look at the images below from the archives of Harold Eugene “Doc” Edgerton of which I’ve tracked certain features to illustrate how arcs naturally occur during locomotion.