The 'technical' name for it is "adonis belt," though sometimes I've heard them referred to as "guy lines" or "sex lines" by girls.
If you want to develop your own adonis belt the first thing you have to do is lower you body fat percentage. For most people, a visible adonis belt would require a body fat percentage of below 10%. If you want to really make them stand out, you could go on a serious cut and aim for a body fat percentage of around 5%.
The second thing you have to do to develop your adonis belt is to develop that specific muscle, which is simply where the lower part of your abdominals meets the lower part of your obliques ("sides"). So, you have to work both your lower abs and your obliques to develop your adonis belt fully.
For me, the best exercise to work the lower abs is the good old fashioned crunch, but done on a decline bench. (Note: these are crunches, not sit-ups.) It's a good idea to adjust the bench so that it is at its steepest decline. I cross my arms over my chest because it helps me focus on my abs, and prevents me from "swinging" my way up. Start from the down position and focus on pulling yourself up with your lower abs, not your upper abs and certainly not with your hips.
Once you have gotten all the way up, don't return all the way down. Just go about half-way or three quarters of the way down. This will allow you to keep your lower abs under the most tension throughout the exercise. I do three sets of these. I started out doing three sets of 50, just recently I have worked up to three sets of 100. The key with this exercise is to push yourself. When your abs begin to hurt, just keep going. Try and go for another 10 or 20 reps beyond where you think you have to stop. You will be very surprised at just how many reps you can force out of your abs. If you do them the right way, you will feel an intense burn in your lower abs, i.e. the area where your adonis belt is.
Another great ab exercise is the weighted sit-up. The weighted sit-up is more of a whole core and whole abdominals exercise, but it will also work your lowers very well also (and thus your adonis belt as well). Again utilizing the decline bench, start off in the down position with a weight on your chest. To start off, you'll probably want to go light. So get maybe a 15, 20 or 25 lb dumbbell. You can also use plates, although the 45 lb plate is a little to big for this exercise. Place it on your upper chest and focus throughout the exercise on holding it there, making sure that it doesn't slide down to your hips. Then, just perform a sit-up as normal, returning all the way down to where your back just barely touches the bench again. But, if you have back problems you may want to avoid this exercise.
Unlike with crunches, you can add weight incrementally with weighted sit-ups, so you don't have to do nearly so many reps. Just do three or four sets of 8-12 reps just like with any other exercise, bumping up with weight when you can do 13 or 14 reps per set on that weight. I started off doing three sets of 12 with a 25 lb plate. Just recently I moved up to using a 75 lb dumbbell, again doing three sets of 12. If you stick with it, you will notice a huge improvement in your abs. It will make your adonis belt "pop out" like nothing else.
For your obliques, the best exercise are sides bends. For this, all you have to do is stand up with a stance that is shoulder width apart or narrower. With a weight in one hand, lean down to your side with the weight in it, and then contract back up. Repeat, doing three or more sets of 8-12 reps per set. The further down you lean, the more your will work your obliques. Try and lean directly to your side, as leaning backwards of forwards will shift the focus of the exercise to your lower back. You can incrementally add weight as you become stronger. You can use plates or dumbbells, but once you get past 45 lbs you will pretty much have to use dumbbells. I started off doing three sets of 12 with 60 lb dumbbells, just recently moving up to three sets of 12 with 95 lb dumbbells.
You have to be careful, however, because an overdeveloped oblique may give the appearance of a love handle in certain situations. So, use the side bend to help develop that "line" on the side of the adonis belt, but don't over-do them. Personally, I try to do side bends just once a week to keep my sides "tight."
A good tool to help with this once you begin using dumbbells are lifting straps. Lifting straps are just straps that you fit around your wrist and then wrap around a bar or dumbbell before you lift. This greatly decreases the load that your forearm must carry, and thus puts the emphasis of the exercise on whatever body part you were trying to work instead of just your forearms. Also, with lifting straps you will generally be able to lift a lot more weight than without, allowing your other muscles to progress (in this case your obliques) much faster than they would have if they were beholden to the progress in your forearms.
If you combine a low body fat percentage with these exercise I've laid out here, you'll see your adonis belt develop very quickly. In fact, if you do everything properly, it will be pretty much impossible for you not to develop a great adonis belt. Hope that helped OP.