The animation library makes many things possible with servos that are otherwise anywhere from difficult to downright implausible. Before we explore the how of the animation library, however, we should more thoroughly explain the why.
Think about the movement of your leg as you take a step. You don't normally have to, but when you do, there's a lot going on in your joints! Your hip extends your leg out, and your knee extends your leg without usually locking it. And your back leg is doing things too; your hip is allowing the leg to move back, and your ankle is flexing. This is a massive oversimplification, but it's still really complicated!
Now imagine each of your joints as a servo, and you have to program taking a step. You cannot control the timing of each movement, because each servo will get to where you tell it to go as fast as you can. You also can't tell when a joint is done moving, so you have to hard-code timings and hope it holds...