Strong abdominals make a great visible impact, particularly when there isn't a layer of fat to conceal them. So the aim should be to develop strong ab muscles and burn the fat off your stomach to show them off. A combination of strong abs and low body-fat is a sign of advanced health and fitness.
Your abdominal muscles enable you to flex your body forwards and also to the side, as well as suck your stomach in. There are 3 main ab muscles:
rectus abdominis
This long pair of muscles, the main '6 pack' muscle, originates in the pubis and extends upwards to insert into the cartilage of the 5th, 6th and 7th ribs on each side, and the xiphoid process (at the base of your sternum, or breastbone). This muscle flexes your trunk forwards, and compresses your stomach.
The 'six pack' (sometimes 8 pack) appearance is caused by bands of tendon which cross the rectus abdominis horizontally, and divide each muscle into 3 or 4 'bellies'. A long band of fibre runs down the centre of these muscles, called the linea alba. This is visible as the vertical dimple running down the centre of a six pack.
obliques
The obliques flex the trunk forward and compress the stomach, and also rotate the trunk. They comprise the 'external obliques' (origin at lower 8 ribs, insertion at front of pelvis), and the deeper 'internal obliques' (origin at iliac crest, or pelvis, and insertion at bottom 4 ribs) each of which act with the opposite 'external oblique' for trunk rotation, and also assist in forward flexion.
transverse abdominis
This is the deepest of the ab muscles, and its sole function is to compress the abdomen, the movement you make when you suck in your belly button. Its origin is at the lower six ribs, and inserts at the tendons of the linea alba (the band of fibre that runs vertically down the centre of the rectus abdominis muscles).
Best exercises for the abs:
The plank - lie face down supported just by your toes and your elbows, and form a 'bridge' with your body, and hold this position. This is the best exercise for your transverse abdominis.
Crunch - great for rectus abdominis (a good variation is the crunch with your feet and knees raised, but the key is to squeeze hard at the maximum contraction, and return to starting position very slowly)
Oblique crunch - for the obliques
Standing side bends - with a single dumbbell in just one hand, lower the dumbbell to your side and return to starting position very slowly. Great for the oblques.
Hanging leg raises - for lower half of rectus abdominus (easy version is to bend at knees, more challenging is straight leg raise) using overhead bar.
Alternate oblique crunch - alternating left leg to right elbow, and right leg to left elbow, this is a more advanced exercise.
Swiss-Ball crunch - perform with someone behind you in case you start to lose balance, and ensure no furniture nearby which could injure you if you fall.