Your core (the middle part of your body) is vital in keeping you upright and stopping you from falling over. If you think of a tower of bricks, the middle part is always the least stable. Your core acts to stabilise this and allows you to remain upright.
The technical part:
Core stability is made up of the transversus abdominis, multifidus, internal obliques, paraspinal and pelvic floor. Core stability is similar to a tent: your spine is the pole, your pelvic floor the stable base and your transversus abdominis the guy ropes. Without one part of this, the pole will fall over.
When the muscles of the core co-contract, they produce force which stabilises the spine. The paraspinals and multifidus act to stabilise the spine. External forces applied to the spine as a result of accident or injury result in contraction of the muscles to support and reinforce the spine, a protection mechanism that is vital to prevent injury and damage to the spine. This support is also needed to allow for movement of the arms and head. Without core stability, we would not be able to stabilise the spine to allow movement and we could collapse.
Most muscles work for short times and then relax. If you think of lifting your arm, the muscles at the top should contract (shorten) to lift your arm, then relax when the arm has moved. These muscles act similarly to sprinters. Your core muscles are your marathon runners. They have to stay active throughout the day and even into the night. They keep going even when you rest.
This means it is important to train your core muscles and ensure they are as strong as possible. Many people have difficulty activating their core stability. The best way to think about it is to think of your core as your internal corset. You are trying to tighten this corset without breathing in. You should be able to hold this contraction for 30 seconds whilst continuing a conversation.
Another way to test your core stability is the bridge:
Keeping your feet slightly apart, you should be able to lift your pelvis slowly and controlled without dropping to one side. You should be able to maintain this position for 30 seconds. If you can achieve this, try and lift one leg up and straighten it. Remember not to let your pelvis drop. Repeat on the other leg.
Here are some other exercises to try: