Teeth are usually thought of as stable, unmoving and stationary. While they are firmly anchored into your jawbone via their tooth roots, teeth are in fact somewhat mobile. They can be moved, and orthodontic treatment makes use of weak and strong occlusal forces to twist, push, pull, and in general move your teeth about to a more favourable alignment than they previously had. To achieve this, braces are put on the teeth which exert force on the teeth and keep the gums in a constant but low level of inflammation, to help make the teeth more mobile. This mobility does not stop the moment the braces come off, and your teeth may feel like they are still moving, because they are.
Usually your teeth set in their new position within a month or so, and they should feel less and less mobile each day. In around a month, their new position should feel quite stable, and you should not experience movement of the teeth. However, there is another problem: teeth tend to shift back to their original position, even if that position is pathological. They can easily do this after orthodontic treatment, as the jawbones are softer and inflamed, and have a harder time retaining the teeth. This is why a retainer is such an important part of the orthodontic treatment, and why the longer the treatment, the more likely you are to wear the retainer, and the longer you will have to wear it.
Retainers are meant to help your teeth set into their new position. During the active phase of orthodontic treatment, the teeth are moved and aligned properly, so that they can bite and chew easily, and they do not interfere in speech, and look neat, and are easier to clean. Once they are shifted to the correct position, it is best to take the cumbersome orthodontic braces off, because they make at home oral hygiene more difficult, are uncomfortable, and cause an inflammation. Once they are off though, the teeth start to shift, and this is when the retention phase begins. During this phase the retainer needs to be worn as prescribed, and it will help with making the teeth less mobile, by setting them, and to help them keep their new place. Wearing a retainer is not optional, and if you want the benefits of orthodontic treatment to stick, you must wear it as prescribed.