An emotion is an autonomic impulse which induces positive or negative mental states. Most sentient species experience emotions, different species attribute different values to different emotions.
The Vulcans suppress all emotion, judging them illogical. However the Vulcans of the lost colony of the Last-of-all-Cities left Vulcan before this practice began and remained a passionate emotional people. This eventually led to the destruction of the colony and following these events the young Spock performed a purging ceremony on himself, fully suppressing what emotions he did have to focus himself on being a pure Vulcan, a being of logic and intellect. (EV comic: "Cloak and Dagger")