Plank, Side Plank, Bridges, Trunk Twists ... These are all Core Muscle exercises that engage a lot more than just your rectus abdominis . There are many muscles that require activation if you want to train your "true core". Your "true core" is comprised of various muscles such as the transverse abdominis, external obliques, internal obliques, rectus abdominis, multifidus, erector spinae, quadratus lumborum, which are surrounded by supporting muscles (psoas major, psoas minor, glutes and more).
The benefits of core training exceed much more than a flat stomach or defined 6 pack. Core strength helps with postural alignment, back pain, core stability, balance, and almost every single sport. Core strength helps prevent core muscles from fatiguing. When those muscles do happen to fatigue, your body is much more prone to injury. Unfortunately, injuries in the core area affect your whole body. (If you have lower back pain, it can feel like your whole body's natural movement is compromised.)
Core Training should be the first priority of full body strength training, which should then be followed by training of the extremities (arms, legs, etc). Whether you are running a marathon, deadlifting 400 lbs, or cycling in the Alps, you need your core muscles to maintain stability. Think of what will happen to your body if you run with a weak core. Your spine will not be supported, which can result in common aggravations/injuries to the lower back.
Core strength can be best measured by how well you can stabilize your core muscles (torso area) while moving your extremities. For example, lift your leg while in plank position and see how well you can keep your hips stationary and squared to the ground. If you can't keep your back flat and your hips stable, it may be because your core muscles aren't strong enough to support your hips. Once you do strengthen your core, your body will be able to efficiently support itself in full body movements. This can help you run/swim longer (due to the absence of lower back pain), movements such as squats, lunges, and jumping jacks will be easier, you'll have better posture when strength training, and you can transfer energy better in full body movements. Think of what your core does while swinging a baseball bat or golf club... it's so much torso/trunk rotation!
Here are some foundational exercises that you can do a couple of times a week to strengthen your core.
plank with leg lift
Try all of these for 30-60 seconds for 2-3 sets each every 2 or 3 days.
enjoy your core!!!