Other forms: runnier
Anything runny is dripping or flowing like liquid. If you have a runny nose, you should probably stuff some tissues into your pocket (or just use your sleeve).
Melting ice cream is runny, dripping from your cone down your arm, and an over-easy fried egg is cooked just enough so that the yolk is a little bit runny. A completely raw egg is obviously runny, and so is the nose of a person with a cold. If you're sniffling and sneezing, your nose is probably runny, or dripping with mucus.