Core Strength
The core is the bridge between the upper body and lower body. Increasing core strength amount to building support beams between one end of the bridge and the other end.
The longer the bridge (such as individual with a long torso) the more support beams (more strength) needed to insure the bridge doesn't collapse under a heavy load.
Thus, increasing core strength amount to building more support beams from between the two end of the bridge.
Doing so provides...
Core Stiffness
The core job is to is to stiffen and prevent motion. This core stiffness allows the hips and lower body to generate more force (Strength and Power) in a movement.
Often when a lifter is attempts to Squat a 1 Repetition Max, you'll here someone screaming to them, "Stay tight"; a reference to stiffening, locking the core down.
Powerlifter are taught to push against the belt in a heavy Squat and Deadlift. Research has demonstrated that doing so provides greater lumbar support.
That is one of the reason that a Powerlifter belt is 10 cm (about 4 inches) all the way around the waist. The larger width allows the lifter a larger surface for the abs to (brace) push against.
Before "Powerlifting Belts", Powerlifter would often turn their "Olympic Lifting Belt", around 4 inches in the back and 2 inches in the front) around. The 4 inch part of the belt in the front abdominal area allowed lifter a larger area to push against with the abs.
"Leakage"
Dr Stuart McGill, one of the leading researchers in core strength, coin "Leakage" as one of the main issues of a weak core; meaning less force (Strength and Power) are generated in let say a Squat with a weak core compared to a strong one.
With that said, the majority of individual should dedicate some time to core training, especially ab training.
Core Exercises
Swings, Rack Pulls, Loaded Carries, and Zercher Squat engage the core (abs) to some extent. These are more effective for increasing low back Strength.
The Incline Press doesn't engage the core that much.
Effective Core/Ab Exercises
Most individual who Squat and prefom Deadlifts, Rack Deadlifts get a lot of lower back "Core Training"; those exercise work the ab but not to the same extent.
Thus, some dedicated Ab Training should be included in a well written program.
Here are some of the most effective Ab Training Exercises...
Inside the Muscles: Best Ab Exercises | T Nation
Rectus Abdominis
Mean: Chin Up, Hanging Leg Raise, Ab Wheel
Peak: Chin Up, Hanging Leg Raise, Swiss Ball Crunch
Internal Oblique
Mean: Ab Wheel from Feet, Ab Wheel from Knees, Bodysaw
Peak: Ab Wheel from Feet, Bodysaw, Tornado Ball Slam
External Oblique
Mean: Ab Wheel from Feet, Hanging Leg Raise, Bodysaw
Peak: Turkish Get Up, Hanging Leg Raise, Bodysaw
Erector Spinae
Mean: Kneeling Cable Lift, Landmine, Reverse Hyper
Peak: Kneeling Cable Lift, Tornado Ball Slam, Lumbar Extension
Final Suggestion
Strength Training for the Abdominal Muscles is no different than training any other muscle group. For strength, the abs need to be trained with heavy load and low repetitions.
There a place for High Rep Ab Training (as with other muscle groups). However, a steady diet of High Rep Ab Training for Strength Athletes isn't going to get job done.
Kenny Croxdale