Tiny jumped in before me on this one - it's not your outer abdominal muscles that are used in riding, it is your core muscles. The muscles which tighten when you cough or as tiny said, go to the toilet. Rather than sucking in your stomach, engaging the core muscles is more like a 'lifting' of your belly button.
Riding with an engaged core is an essential part of effective riding. If your core is not engaged, your seat will not be effective, (i.e. you will not have an 'independent' seat) and in the case of dressage, it will be near impossible to achieve any sort of half halt which leads to engagement and collection of the hind quarters.
The core muscles keep you upright in the saddle, allow your abdominal area and pelvic area to absorb the motion of the horse's movement and allow you to slow and speed up your own tempo to control that of the horse.
It is not a case of just bracing your core muscles from the moment you get in the saddle. As MBP said somewhere above, the degree of engagement of the core muscles depend on what you are doing in the saddle. If I am warming a horse up in a working, rising trot, allowing the topline to stretch down and out, my core will only be engaged enough to keep my upright and solid in the saddle. However, if I am beginning lateral and collected work, (and no, I'm not referring to just being on the aids, I'm talking genuine collected work), such as shoulder in, half pass or pirouette work, my core will be burning by the end of the session as the core muscles are what controls your seat and ability to 'hold' the horse together while maintaining energy. Trying to keep a big moving warmblood together in sitting trot and canter absolutely requires a high degree of core strength or you will never get anywhere!
A few exercises to help with your core strength, both to make you stronger and to be aware of when your core is engaged and when it is not -
1. A brilliant exercise for strengthening the core muscles is the 'plank'. Get onto the ground as though you are going to crawl like a baby. Rest on your elbows and toes, with your forearms facing straight ahead and elbows located directly under your shoulders. Raise your torso so that your body is dead straight and resting on your elbows and toes - do not arch your back or stick your backside in the air.
This will force you to hold your core muscles - and hell will you feel them!! Practice daily, most 'normal' females should be able to hold this pose for around 1 minute. As a dressage rider, I know my core strength is lacking if I cannot hold it for more than 5 minutes!
2. On the horse, and this one is a little 'rude' but works well. So sitting in the saddle, keep your ear-shoulder-hip-heel line. CLose your eyes and imagine you have a straw in your 'lady bits'. On the saddle there is a green pea (the vegetable ;) ) , and you need to suck it up with the straw. Your core muscles will activate if you are 'sucking' effectively!!
3. This can be done in the saddle or on the ground using a length of rope for reins. Hold the reins as though you are riding and get a friend to hold the other end of the makeshift reins. Relax your core muscles and let your torso go 'soft'. Have your friend pull the 'reins' forward without you letting go of the reins - you will almost certainly get pulled forward.
Now repeat the exercise, but keep your core engaged. I bet you will remain upright.
Hence - keeping the core engaged is also a safety consideration on a horse. A horse can suddenly reef the reins from your hands, or buck, trip etc. and if you do not have an engaged core, more than likely you're going to eat dirt. If the horse does the same and you have an engaged core and effective position, you're going to stay firmly in the saddle and be able to combat the problem.