Often your body language can connote or imply how you feel without you having to saying it directly. For example, if you fold your arms and look away from someone as he speaks to you, you are connoting your discomfort.
When you act a certain way to show how you feel rather than just outright saying it, you're connoting or suggesting that emotion. Words can often connote or suggest certain meanings or ideas. The word turbulent connotes the image of a bumpy ride on an airplane, for example. Connote is also used in formal logic. If A connotes B, then for A to be true, B has to also be true.