In the process of diffusion, what is moving and in what direction does it move?

A substance from higher concentration to lower concentration

Materials always move from an area of high concentration to an area of low concentration in diffusion. What moves is the substance with the uneven concentration gradient.

For example, water diffuses (we call it osmosis, but the principle is the same) from higher concentration to lower concentration. If a blood cell is placed in distilled (pure) water, the water is hypotonic to the cell, meaning the concentration of pure water is greater outside the cell than inside. Water will flow into the blood cell, seeking equilibrium, and the cell may swell until it bursts.

On the other hand, if a blood cell is put in a highly saline solution, the concentration of water will be greater inside the cell because it is now in a hypertonic solution. Water will flow out of the blood cell, causing it to shrink and perhaps die.

Water isn't the only substance that diffuses; this is just an example. The bottom line is that a substance will move from an area of high concentration to an area of lower concentration until an equilibrium is reached, if possible. This is called the concentration gradient and it is what propels diffusion in one direction or another.

Gas particles move from a region with high concentration to a region with low concentration along a concentration gradient

(Concentration gradient just means from high to low concentration)