Still waters run deep is an idiomatic phrase meant to imply that someone who is calm or quiet may nonetheless be quite interesting and intelligent. According to Dictionary.com, this phrase has been in use as a figurative statement since about 1400.
Taken literally, saying that still waters run deep can mean that a river that runs smoothly isn't necessarily shallow. The idiomatic expression takes this concept and applies it to people. A person who is not particularly gregarious and demonstrative isn't necessarily quiet because he or she is stupid or dull. Rather, a person in whom still waters run deep can be a deeply interesting person who maintains a calm exterior.