Have you ever found yourself trying to run from something scary, or swim to the surface of the water only to find that no matter how hard you struggle your body weighs three tons? You're dreaming. And then, hopefully, you wake up.
Some say that this is a lack of self-confidence manifesting itself in our dreams. Others say that the brain is running simulations for dangerous situations in a risk-free dream environment. Whatever the case may be, we sometimes see our dream-selves throwing ineffectual punches, and overall failing at physical challenges.
I'm not sure whether it's possible to give a conclusive explanation for all cases of dream-weakness in all people, but I think I can explain many cases of it including my own.
When we are in REM sleep (where dreaming takes place) our brain turns off all motor functions. This state is called nonreciprocal flaccid paralysis. This is useful to us so that we can be motionless while we sleep and dream, and not "act out" our dreams. (We toss around in Non-REM sleep).
Personal Example: One night I found myself in a dream doing the workout I had planned for the next afternoon. In the dream I was failing miserably, though I knew the challenge was not beyond me. And then I woke up.
I figured it out. My brain was not receiving feedback that my muscles were moving (motor functions were turned off), and that manifested in the dream as weakness. It was simple. I was able to figure it out because my dream-weakness was caused by something practical (and something that I had done before) and not having to run away from a monster.
So the next time you wake up feeling weak or ineffectual, remember that it's a lie from the depths of your brain.