What does flexing a joint mean exactly?

See below. All joints have different types of movement. For instance, the elbow has only the ability to flex and extend. To flex the elbow, you bring the hand close to the shoulder. To extend the elbow, you straighten it out again. Flexing the hip brings the knee close to the belly, extending the hip straightens the leg out. Hope that helps.
Flexing. Flexing a joint is that activity which brings the bones that form the joint in closer proximity to each other. For example flexing the right elbow joint describes that movement when the right hand is moved to the right shoulder, narrowing the angle made by the lower arm meeting the upper arm.