‘Core, trunk, midsection’ strength is necessary for using the full potential and reducing the risk of injury in sports but it is also key factor in health and fitness of general population. Development of the strong ‘core’ should be part of any strength and conditioning routine and fitness program. There is many variations of abdominal exercise and also many mechanics how the strength in the ‘core’ can be trained. (Check the link for more info about different ideas on the core mechanics and training: http://breakingmuscle.com/mobility-recovery/how-are-we-still-getting-it-wrong-abdominal-hollowing-vs-bracing)

Think of the ‘midsection’ being the chain link connecting upper and lower body. If the link is weak it can get broken once the force is going throughout this link to the distal parts of the chain. In reality we hardly break our back. However weak link can cause inefficiency and lack of stability for movement which can lead to bad performance and injury. This is happening even in so basic movement like walking.

Core is same as other groups of the muscles and it is trainable through the approach of consistency, variability and progressive loading. As with other exercises you start with comfortable intensity and then gradually(linearly or nonlinearly) adding the load. And also making little adjustments to the exercise.

There are few basic progressions which an be effective in developing strong core:
Stability-Ball Rollouts/stir the pot
http://youtu.be/VJv2winv5oE
Trx roll outs
http://youtu.be/s0z8X0l_JYw
Body saw trx
http://youtu.be/R8QwySflzLQ

There are obviously many option and once you grasp the concept only sky is the limit in creating interesting exercises. Remember to starts simply and progress from easy moves to more complicated slowly.