When you are walking or speaking, there is an effortless in your psychology. You aren't trying to do those things - you just do them. We don't see those acts as difficult, so we do them without thought. They become automatic. We do thousands of acts like this - all of them requiring complex body movements - and yet, we percieve them as easy.
In terms of playing the classical guitar, many of us perceive playing as "difficult". We may even have teachers or collegues who like to encourage this idea. The interesting point is - because we perceive it as difficult, we tend to make it more difficult than it actually is. Our bodies tense up for passages that are no more complex than typing fast or speaking. However, our perceptions are programmed to see great difficulty in it.
If we think that moving our hands/fingers is "easy" (like walking, speaking, or driving), it lightens the psychological "weight" of the act and we can move much more freely. We might still miss the passage for now, but the psychological and physiological freedom that is attained far outweighs the mistake. In fact, we will begin to play better much more rapidly if we start to see playing as "easy".
However, if we add heavy psycological weight to the same action (with thoughts like - "this is difficult, i never get this part, i want to get this perfect", etc.) then the act becomes overly dramatic - full of tension and fear. The hands and body tense up. It becomes more difficult to play because your body is reacting to your thoughts. Your thoughts are basically telling the body "this is a difficult situation" - and the body simply agrees with you.
While walking, talking or doing any other act that is natural to you - notice your mental state. Notice how easy it is and how you feel. Feeling is everything. Notice how you flow. It feels good in the body AND the mind. The same goes for playing. If you feel good psychologically while you play, you must inevitably play better. Don't wait to get the passage right first to feel good - feel good NOW - regardless of how things sound. Believe the passage is easy in your mind no matter how difficult it may seem. You'll notice with time how it gets easier - your body begins to react to your mind.
The body (hands epecially) represents your mental state. You can work on relaxing the body or hands as much as you want, but if you don't relax your psychology while playing, the body will keep slipping back into tension and difficulty.
The body mirrors our psychology. Feel good now.