Diffusion is the spreading out of particles from an area of higher concentration to an area of low concentration.
Diffusion happens in both solutions and gases, because the particles are free to move around randomly in these substances.
Temperature and a higher concentration gradient (difference in concentration) can both affect the rate of diffusion. When exposed to a higher temperature the particles have more energy so they're able to move around faster.
Osmosis is the diffusion of water particles from a dilute solution to a more concentrated solution through a partially permable membrane.
For example, if a piece of potato was dropped into a concentrated salt solution the potato would lose mass, as the water particles would diffuse out to the more concentrated area.