What they are and what they do:
External oblique: The external oblique is situated on the lateral and anterior parts of the abdomen. It is broad, thin, and irregularly quadrilateral, its muscular portion occupying the side, its aponeurosis the anterior wall of the abdomen. The external oblique functions to pull the chest downwards and compress the abdominal cavity, which increases the intra-abdominal pressure as in a valsalva maneuver. It also has limited actions in both flexion and rotation of the vertebral column. One side of the oblique is contracting can create lateral flexion. It also contributes in compression of abdomen.
Transverses abdominis: also known as the transverse abdominus, transversalis muscle and transverse abdominal muscle, is a muscle layer of the anterior and lateral (front and side) abdominal wall, which is deep to (layered below) the internal oblique muscle. It is thought to be a significant component of the core. The transversus abdominis helps to compress the ribs and viscera, providing thoracic and pelvic stability. The transversus abdominis also helps pregnant women deliver their child.
Internal oblique: is the intermediate muscle of the abdomen, lying below the external oblique and above the transverse abdominal muscle. The internal oblique performs two major functions. First, it acts as an antagonist (opponent) to the diaphragm, helping to reduce the volume of the thoracic (chest) cavity during exhalation. When the diaphragm contracts, it pulls the lower wall of the chest cavity down, increasing the volume of the lungs which then fill with air. Conversely, when the internal obliques contract they compress the organs of the abdomen, pushing them up into the diaphragm, which intrudes back into the chest cavity reducing the volume of the air filled lungs, producing an exhalation. Secondly, its contraction rotates and side-bends the trunk by pulling the rib cage and midline towards the hip and lower back, of the same side. It acts with the external oblique muscle of the opposite side to achieve this torsional movement of the trunk. For example, the right internal oblique and the left external oblique contract as the torso flexes and rotates to bring the left shoulder towards the right hip. For this reason, the internal obliques are referred to as "same side rotators."
Rectus abdominis: known as the "abs," is a paired muscle running vertically on each side of the anterior wall of the human abdomen, as well as that of some other mammals. The rectus abdominis is an important postural muscle. It is responsible for flexing the lumbar spine, as when doing a "crunch". The rib cage is brought up to where the pelvis is when the pelvis is fixed, or the pelvis can be brought towards the rib cage (posterior pelvic tilt) when the rib cage is fixed, such as in a leg-hip raise.
Multifidus: consists of a number of fleshy and tendinous fasciculi, which fill up the groove on either side of the spinous processes of the vertebrae, from the sacrum to the axis. The multifidus is a very thin muscle. The multifidus muscle allows each vertebra to work more efficiently, and as a result, the muscle guards against spinal joint degradation. The posterior branches of the spine innervate the muscle at various locations.
Gluteus minimus: the smallest of the three-gluteal muscles, is situated immediately beneath the gluteus medius. It is fan-shaped, arising from the outer surface of the ilium, between the anterior and inferior gluteal lines, and behind, from the margin of the greater sciatic notch.
The fibers converge to the deep surface of a radiated aponeurosis, and this ends in a tendon, which is inserted into an impression on the anterior border of the greater trochanter, and gives an expansion to the capsule of the hip joint. It is also a local stabilizer for the hip.
Erector spinae: a deep muscle of the back; it arises from a tendon attached to the crest along the center of the sacrum (the part of the backbone at the level of the pelvis, formed of five vertebrae fused together). When it reaches the level of the small of the back, the erector divides into three columns, each of which has three parts. The muscle system extends the length of the back and functions to straighten the back and to rotate it to one side or the other.
Quadratus lumborum: is a muscle in the lower back. It is irregular and quadrilateral in shape, and broader below than above. It contributes to the stabilization and movement of the spine and the pelvis.
Gluteus medius: one of the three-gluteal muscles is a broad, thick, radiating muscle, situated on the outer surface of the pelvis. The gluteus medius and gluteus minimus function together to pull the thigh away from midline, or "abduct" the thigh. During gait, these two muscles function principally in supporting the body on one leg, in conjunction with the tensor fascia latae, to prevent the pelvis from dropping to the opposite side.
Just what they do:
Piriformis: The piriformis muscle is part of the lateral rotators of the hip along with the quadratus femoris, gemellus inferior, gemellus superior, obturator externus, and obturator internus. The piriformis laterally rotates the femur with hip extension and abducts the femur with hip flexion. Abduction of the flexed thigh is important in the action of walking because it shifts the body weight to the opposite side of the foot being lifted, which keeps us from falling. The action of the lateral rotators can be understood by crossing your legs to rest an ankle on the knee of the other leg.
Coccygeus: The function of the coccygeal muscle is to support the all of the organs located in the pelvis. In females, this includes support of the uterus. This muscle also closes off the back of the pelvic cavity.
Levator ani muscles: The levator ani muscles act as supporting structures in urinary control, having both involuntary and voluntary functions.
Iliococcygeus: pulling the coccyx from side to side and elevating the rectum.
Pubococcygeus: Aids with core and stability.
Puborectalis: made up of skeletal muscle and its function can be manipulated by posture and conscious thought.