While standard braces are used to change the position of the teeth, removable appliances are used to maintain the teeth in their new positions. Sometimes they are also used to dictate the growth direction of the jaws in order to achieve suitable changes in facial profile. They can be used prior to, and in combination with fixed appliances.
Not all orthodontic cases require the use of removable appliances. It takes great skill and experience to know the conditions that require the use of removable appliances. It is also not just about the use, timing the treatment rightly is also necessary.
In as much as you are free to remove these appliances for one reason or the other, you must ensure you wear them as instructed, else there is the risk that your muscles, teeth, and jaws will revert to their former positions.
When you first start wearing these appliances, you may find out that your speech and chewing patterns have been affected. You may also drool a lot. You only need patience to get adapted to it. You must handle all removable appliances with care.