That is a great question. Most of the equine world uses the term "heels down" as though it's Gospel, which I guess it has become. But before you just accept this though, let's think it through. The human brain most of the time, will interpret a command and then try to do it. When someone says, "keep your heels down" your brain typically pushes your heels down against the stirrups. Just try sitting down in a chair, and keep your heels down....What happens? The goal of this is to improve your seat, which is a good goal but the statement and end result is usually not good, at least in the beginning. Why?
When your brain tells your heels to go down and pushes to keep them down, you're actually tightening up your whole lower body from the lower back down through your legs because you're using your muscles. In order to really be a good rider, you need to have a relaxed body not a stiff one. Partner that with the fact that most beginning horseback riders end up tightening their bodies when they instinctively go into the "cradle position" we talked about already, you are creating a position that just does not work easily. So just what might be the answer to this desire to have a good seat using a part of the foot?
Keep your toes up! Now why would this be better than keeping your heels down? Because when our brain hears toes up, it just naturally lifts the toes and the rest of our lower body remains relaxed except for one important part. The leg part that does do something is our hamstrings. With our toes up, our hamstrings are at the end of their extension, and if you instinctively try to cradle like most folks do, your own brain signals discomfort and you wont end up over the front of the saddle or horse. So it's really a natural way to tell your body what to do without causing unwanted side effects.
It also gives your body natural resistance, so that you have a greater amount of control over your own body, while the horse is moving it around. You should practice lifting your toes all of the time while on your horse, from the walk to the trot to the canter. Please note also when you lift your toes, your heels automatically go down but your aren't using muscles to achieve it! So the Gospel is fulfilled using a new path!
Now when you partner leaning back according to the Laws of Motion when you trot and canter and keep your toes up for the reasons mentioned above, it gives you the best position of your body and control of your own instincts to have a much better chance of relaxing and moving with the horse's own movement. Once your brain senses that you are in balance, your body will relax and you will naturally start to match the horses rhythm with yours and the picture others will see is someone that is riding their horse in balance.
But what if I lose my stirrups keeping my toes up? It is perfectly alright to lose your stirrups as they are not suppose to be part of your balance. The stirrups are there to mount and dismount your horse, and to occasionally rest your legs. Folks that constantly use or are taught to use their stirrups as a way to keep in balance, are the same as ice skaters using the wall as part of their balancing. Learn to ride in perfect balance without the aid of anything but your own brains ability. Using the Laws of Motion by leaning back against the horse's momentum, and keeping your toes up are the 2 simplest ways to gain balance and improve your seat from the very first day you ride! OR you can take 1 to 2 years of lessons fighting the Law, riding unbalanced, spending endless dollars on lessons and maybe, just maybe still be out of balance.