Any time you witness one substance gradually spreading, that's diffusion.
Sometimes this is a gas diffusing in another gas. If yoyou leave the lid off a bottle of perfume, soon the whole room will smell - because of diffusion. If your nostrils have ever been the unfortunate recipients of flatulence that has spread through a room, you've also experienced it.
In terms of liquids, make yourself a cup of tea. Literally. Then watch it brew. The "tea" (or, more correctly, the tannins in the tea) will start out strongest nearest the tea leaves, and then spread out from there.
Regardless of the type of diffusion, it always occurs randomly, and will continue until dynamic equilibrium is reached.