Rhythm - how the actions or "beats" in a shot are spaced out over the length of a scene. You might also call this "tempo". Unlike with music, good animation has an inconsistent rhythm, making it less predictable.
Texture - the variations of timing and poses in your shot. Big and little actions, slow and fast timing, flurries of action and holds. A shot in which all the actions are the same size, have the same timing, and occur in an even rhythm has no texture.
Take a look at this clip from the classic Disney double-feature, "The Adventures of Ichabod and Mr. Toad". Here we see the hero, Ichabod Crane, wooing Katrina and evading fellow suitor, Brom.
There is plenty to be appreciated in this clip, but let's pay attention to the rhythm first. Notice how the first 4 pose changes on Ichabod are all timed about the same and are all spaced evenly in time - you can count out loud between the beats: "1-1000, 2-1000, 3-1000, 4-1000". In animation we generally try to avoid this kind of evenness in the timing; in music, a consistent rhythm is a good thing, but not in animation.* There's a method here, though: the animator is establishing a pattern so that he can break it. He gets the audience used to a certain rhythm so that when he changes it the audience is surprised. When Brom appears suddenly and tries to grab Ichabod the scene shifts into high speed. This contrast of rhythm creates emphasis - we know something important just happened. It's such a fast change that if it weren't staged perfectly, the audience would miss it and wouldn't understand the action. Notice how Brom hits his "grab" pose and holds it, and how Ichabod's hat floats in the air to tell you where his head "was", since there was no anticipation into his drop.
My favorite part of this scene is the next shot, where we cut inside the house and Ichabod is standing completely still, as if nothing just happened. The action of lifting his hat is tiny compared to all the big flourishes and the escape that proceeded the shot, and is isolated to just his arm. It's another big change in the rhythm and phrasing of the scene, and it not only reiterates Ichabod's composure in front of women, but also adds unexpected entertainment value. A few more quick actions (grabbing and presenting the flowers), and the sequence ends with Ichabod melting into a relaxed pose. All these changes in tempo, size of action and timing give the scene its texture.
The above clip is a pretty broad example, but you can achieve the same kind of texture in a smaller, simpler scene. Here's a clip from Monsters, Inc. featuring Sully, who is reacting to an offscreen sound.
Essentially, Sully is doing the same action over and over: he is looking around for the source of the sound. However, the animator has given the shot texture by varying the timing and size of the looks, as well as breaking up their distribution over the course of the shot to give it a more organic, staccato rhythm. Notice also that there is a progression in the looks; they start small, just in the eyes, then move on to progressively bigger and bigger moves involving the head and the torso. There's even a double-take to break up the tempo even more. The final look is the largest, and involves the biggest shape change in the body by incorporating the screen left arm. This gives the final look the most emphasis, because it's the point of the shot; this is when Sully will actually see the source of the sound (Boo playing with his tail).
Planning and blocking and animated scene is a complicated undertaking, and there are many things to keep in mind. It's not enough to obey the 12 animation principles. It's not enough to have original acting ideas and clear posing. You have to figure out the best combination of all these things to create your performance. Memorizing the dictionary and grammar rules does not make you a poet! You must find ways to string your ideas together lyrically to create a clear, cohesive, and of course, entertaining performance. You may come up with 4 great ideas for your shot, but the ideas might not flow together well. As important as your acting ideas are the changes between your ideas. What's more, the shot may only need 2 ideas. Try to be economical with your ideas, and find a sequence that flows together well. Figure out how little you need to do in the shot.
I usually start by just throwing out every idea I can on paper and/or video tape. Next I narrow it down to my favorite ideas that I think are most appropriate to the shot. From these I try to find the ideas that flow together naturally and create a nice progression, making sure that the biggest change occurs at the right time to emphasize the point of the shot. Once I have this phrasing worked out, I start to block my poses and actions into the computer. Now I can start to experiment with timing, playing with the speed of the individual actions and moving my beats around in time to try to break up the rhythm of the shot. The computer is great at helping you figure out your timing without wasting a lot of effort. This is how I find the texture in my animation. Usually after I've done my first blocking pass, I'll end up adding or removing an idea, or changing something from what I had planned to make it work better in the actual 3D scene. But no matter what I always play back the entire scene to make sure it has a pleasing texture. Always check the texture not only across the single shot that you're working on, but across the entire sequence. Remember to look at your work in context!
* What if you're animating to music? If a character is singing or dancing you want to respect the overall rhythm of the music, of course, making sure you regularly accent the beats of the music. But you must also look for places where you can add accents that fall outside the music's tempo. If you stay slavishly locked to the same beat, the animation will quickly become boring to watch. Have some accents fall on down beats, some on upbeats, some between beats. Have some actions happen in double-time, some in half-time. Remember that whenever you stray from the tempo of the music, you create emphasis, so do it wisely! Check out this vintage Flat Eric clip:
Note how he hits the down beat for most of the clip, but occasionally he breaks into a new rhythm, or skips a beat for emphasis (around 00:23). These little changes in the rhythm keep the clip entertaining to watch.
Thanks for reading!