Where does the physical engine come from in almost every natural being? Whether you are human, volcano or other living thing your core is where the kinetic energy starts to be unleashed. A person's core aids absolutely every single type of exercise and general movement so it's only natural to develop your core as much as possible. Your core which is located where you would imagine your diaphragm would be, needs work, needs stimulus in order to be strong to develop.
What is the best way to develop core? Whilst almost anything to do with fitness would naturally help with core especially if you focus more on form than anything else, the name of the game when it comes to development of the vital area is stability. If you want to develop a strong core you must develop stability and balance. Think of your core as the load bearing plank of wood, the corner stone to everything else that holds you up. A weak core will not hold up a strong structure and a significant weight applied will make the house come crashing down. Therefore the best way to develop core is to focus on exercises that force you to practise balance either under weight or with none at all and focusing on longevity. the main point is you must focus on both absolutely and with similar time spent on both.
Core work is not necessarily just ab work, but that type of workout is indeed important when developing core strength. Ab workouts with an element of balance are in essence the best combination to work on the core and application of that core strength to workouts you do anyway. Of course this isn't limited to just ab workouts but any workout in which the abs and core are used a lot; for example running uphill where you are essentially balancing on one leg at a time whilst running up hill thereby using your abs as well as your legs to push you up and keep your back straight. Working core strength into exercises makes for a much more efficient workout.
A strong core aids in the basic strength exercises too; when you squat, dead-lift and chest press your core is used heavily. With a weak core your form goes first and then aches and pains follow. Balance and stability are the two words that go together with core. A straight back, awareness of where one's hips are, the balancing of weight around the body rather than one individual point are what makes for a good core. The benefits are fantastic.
When you breathe do you raise your shoulders? when we get tired the tendency to do just that is increased. An indicator of good core strength is the ability to breathe deeply without raising our shoulders but instead expanding the stomach. The longer you can do that without resorting to bad breathing means your core is indeed developing.
Essentially you need to make a self-assessment of yourself; where is the strength coming from? Is it coming only from the muscle being used? Or does the strength originate from the core muscles of the abs, the TVAs, the pelvic muscles, the lats etc? Make sure you diagnose whenever you workout. As workouts get harder, a nd as you get tired it is the core that keeps you going, keeps the form up and keeps the efficiency high. Working on the core is vital and doing it right makes a lot of a difference when improving and going forward.