An elliptical machine has two slots in which to put your feet, which move along half-crescent, or "elliptical," tracks. Many also have handles connected to the tracks, which allow working of both the upper- and lower-body muscles.

Lower Body

All elliptical machines target the lower body. There is less harmful impact on the legs than on a treadmill because the feet are never lifted from the ground and therefore don't slam back down with force.

Upper Body

Many, but not all, ellipticals have moving handles that are connected to the foot pedals. By gripping on onto these handles during the workout, you can engage your upper body muscles, notably your biceps and anterior deltoids (shoulder muscles).

Targeting the Hamstrings

To focus muscle development on the lower body, use an elliptical without moving handles, or simply refrain from grasping the moving handles. Be sure to grasp the stationary handles for safety. This will put all of the work on the legs, especially if you refrain from bouncing. Increasing the resistance on the elliptical to a moderately challenging level will ensure that the posterior leg muscles such as hamstrings and glutes become engaged.

Targeting the Quadriceps

Just as with posterior muscle targeting, you can target the anterior leg muscles, such as quadriceps, by grasping the stationary handles and increasing the resistance. The difference, though, is that you go backwards. This reversal of motion engages the opposite muscles the legs.

Other Muscles

You can also engage the abdominal muscles on the elliptical by tightening them during the workout. Challenge yourself to not bounce while on the machine by clenching the abs. The elliptical also engages the most important muscle of all--the heart muscle. Moderate, sustained work on the elliptical several times a week can lead to greatly improved cardiovascular health.

Source:

Elliptical Training: Elliptical Review

Resource:

Information on benefits of going backwards