
A crucial factor when animating is the ability to draw your audience into the world you are portraying. One of the most effective ways to do this it to make things move in a way that seems believable to them. If you want the audience to feel the impact of a boulder landing on a characters head, then you need to know how you can manipulate the medium in order to make the boulder move in a way that looks heavy and dangerous when falling.
In my teaching experience students seem to underestimate the value of this principle. Often they believe that making the boulder look more like a boulder is the best way to convince the audience of its authenticity, but this represents a basic misunderstanding of how the human brain is wired. We respond much more to movement than detail, so a skilled animator can make a simple circle with no detail move in a way that convinces us it is big and heavy, but a very detailed representation of a boulder that floats to the ground unnaturally will never convince us that it is really there. I am not saying that the movement has to be realistic, it can be a caricature or abstraction of movement that still effects us, but achieving this still requires that the animator understand how physics is affecting the object they are animating.
Animators need to constantly hone their understanding of timing, spacing, squash, stretch and arcs so as to develop an intimate understanding of how to represent the movement of objects and characters in a way that is that engaging.

Jean-Denis Haas explains why animating the bouncing ball is central to understanding animation principles.

AM student Sandy explains Slow in and Out, showing things speeding up and slowing down.

Dermot O'Conner explains how to show weight through the classic bouncing ball exercise

Another bouncing ball example from Larry's Toon Institute. Part1. Part2.

Squash and stretch in a jump.

The undeniable power of arcs.

Jason Ryan's video tutorial on Anticipations, Paths and Actions. (if asked for a password just type JRA)

The Animation Physics web site. This isn't just someone saying this is how I do it, this is someone saying this is how it really happens. Check out the Tutorial section for clear concise illustrated notes on how stuff moves.

The Rainplace Blog has a great series of posts on squash and stretch, its in 3 parts (Part1, Part2, Part3).