Ok...time to play a little game of "what's it do?
So have a look at the picture here on the left and see if you know what it is. Of course, you probably know it as "the abs" or the "six pack". For the science nerds, it's also referred to as the Rectus Abdominis (see why saying abs is easier?)
Just what does this muscle do anyway? The "abs" are connected to the pelvis at one end and ribs 5 through 7 at the top end (remember this because it will come into play later) The abs can do 3 things when they are activated (or flexed) They can flex the spine such as you see when performing a crunch, they can laterally flex the spine such as you see when to bend to the side and they can also rotate the spine such as you see when you...well, when you rotate the spine.
Remember when I mentioned where the abs attach to your body? Notice I didn't say that the abs attach to your legs in any way. Why this is important is that when you see people doing exercises such leg raises of any sort thinking they are working their abs---they are not. Leg raises are not an ab exercise. Leg raises do not isolate the abs in any way. People often think they are working their "lower abs" by doing leg raises. They aren't! It's impossible because the abs do not attach to the legs.
This brings up another good point. If leg raises don't work the lower abs, then what does? Well, there isn't one that works the lower abs directly. That's because the abs are all one muscle. You either work all the abs or none at all. You can no more work the lower abs than you can the lower bicep...or just the middle of your triceps...or just the upper left corner of your glute max.
However, there is a great exercise you can do to strengthen the abs. Studies show that one of the best ab exercises is-----drum roll-----the crunch! And as a bonus, doing a crunch on a stability ball creates even more muscle activity than the regular crunch.
One last parting thought. Will doing tons of crunches finally give you that elusive 6-pack? Not quite. No matter how strong or toned your abs are, it's the layer of fat in front of it that prevent you from seeing them. Most people with 6-pack abs are carrying a very low body fat percentage. Generally, you would need somewhere around 10% or less body fat to see your abs. To put this in perspective, a healthy range for men is between 13-16 and for women it's 20-30%