There are two types of effleurage -- superficial and deep. Superficial effleurage uses a light touch and is very soothing. This is the kind of pressure you get at the beginning and end of the massage. This gentle pressure gets you accustomed to the therapist's touch, and prepares you for the end of the massage. It is also used between other strokes to clear the area and soothe the intensity of deeper strokes.
A massage therapist generally applies massage oil using superficial effluerage, a hand-over-hand gliding movement.
Deep effleurage, or deep gliding, uses more pressure, stretching and broadening the muscle tissue and fascia. Deep effleurage follows the direction of the muscle tissue. Generally the movement is towards the heart, with the return stroke being much lighter and away from the center of the body. It warms up the muscle tissue, preparing it for even deeper, more focused massage.
If the practitioner uses too much force during effleurage, the body will tighten up protectively. So be careful about asking therapist to "go deeper", even with deep tissue massage.