This is a kinesiological term that refers to active contraction of a muscle while it is lengthening.
In weight lifting, this is the type of contraction that occurs during the "negative" phase of a repetition when the weight is returned to its starting position.
In pitching, the forearm may experience centripetal force that slings it laterally away from the body. This slinging action is called forearm flyout. To prevent injury, the brachialis muscle eccentrically contracts against this centripetal force. While contracting, the muscle lengthens to allow full arm extension.