I'm in a similar situation, looking forward to hearing some answers to this... I've got a cute bare-ly there 4-pack (lol) but I'm looking for ways to up the ante and really get some definition.

It comes down to body fat, muscle mass and genetics.

But it also depends on how MUCH definition you're talking about. Fitness models who look like they've been vacuum sealed don't look like that ALL the time, only when preparing for a photo shoot or competition. Lighting, spray tans, flexing, a great photographer and a little help from Photoshop (I'm not talking about total re-editing of a photo, but changing just the color balance and values can make a big difference) never hurt, either.

For instance: Same model.

LIfting and cardio in general for exercise, but what's really critical is diet and one's genetics. There are people around who don't do anything particular for their abs because they're lean there in the first place, and lots of other people who can do all the right things but have to work MUCH harder with their diet because of their natural tendency to store fat in the midsection. Body type comes into it too(genetics), as in torso length. A short-waisted person is going to appear to store more fat than a longer-waisted person simply because there's less room for the fat to go length-wise, so it goes OUT, hiding those abs underneath. I have this situation myself. All that said, anyone can definitely IMPROVE the appearance of one's abs by way of scrupulous diet, lifting weights, cardio, and let's not forget Pilates training which is par excellence for core conditioning in general.
OK, back to diet - bodybuilding/fitness competitors and fitness models often go on very strict diets and increased volume of workouts before their event, and for many, they don't look like that all the time, although even in their non-event season they sure look pretty good to the average person who is struggling. Diets are usually very low-carb and often very low-fat as well, with a re-feed just before the event to fill out the muscles after fat and water have been lowered. That part about the water is tricky - do it just right, and one looks awesome, do it wrong, and one ends up dehydrated and with muscle cramps. So this IS a very transitory state that can't be maintained.
Bottom-line, abs are made in the kitchen, then the exercise. One can always and so easily out-eat one's workout, especially if one is eating the typical high-calorie junk food American diet. So it does take some real effort diet-wise!

I am now on a [mostly] "clean eating" diet and I'm starting to enjoy the burn when doing core exercises (however, I have a decent amount of muscle under the fat already) so I'll see if these combine into killing that pouch. When it comes to lifting, I am doing bicep curls, triceps extensions, and squats with shoulder presses..is that okay or should I work on something else? I'll try to do more and more push-ups and I don't know the name but where you put your hands behind you on a bench with your legs straight, feet on the floor and dip your body down and push back up..

low body fat and genetics.