Understanding the concepts you are working will allow you to build a compelling puppet instead of a static statue. Computers have limitless problems and a limited number of things they can accomplish. For right now, it's still relatively easy to bring a machine "to its knees" and turn itself off.
You're going to have to know a little bit about blood and guts to avoid this. Not just the anatomy of muscles, sinew and fat...but also the internals of your machine.
- How does a matrix work?
- How do you animate a rolling cube?
- The difference between a hierarchy and a constraint?
- Why is order of execution important?
- How do you use texture space efficiently?
- What is the renderer actually doing?
- Why are expressions useful and how do they work?
- Why shouldn't you put a million points on that line?
This type of nuts and bolts knowledge will make you more efficient as a character engineer. And the more efficient you are, the more ambitious you can be with your character.
Spend all your polygons in a place where they won't be useful and you won't get to make those sexy tear ducts you always wanted.
The best advice I can give you is to get really intimate with whatever software you use.
Understand what is actually going on when you move that point. After you've learned a few packages, you'll begin to realize that under the hood most pieces of 3D software are doing the same types of things--only their workflow concepts, interface and design are different.
Learning such fundamentals will help you avoid pitfalls and become a better character engineer.