You can expect a little bit of discomfort as you get used to wearing your aligners—after all, you’ll have something completely new and unfamiliar in your mouth for extended periods of time.
Beyond that general adjustment period, there’s also typically some soreness during the first few days you wear each new set of aligners. When pressure is applied to a tooth to initiate movement, the periodontal ligament surrounding it is stretched on one side of the root and compressed on the other. That causes inflammation as the body tries to heal, but it will only last for a few days before the much less uncomfortable bone-remodeling phase of each step of treatment begins.
One good way to deal with soreness is to use the Chewies that come with your aligners—just put them in the affected area of your mouth and bite down repeatedly. That will exercise the periodontal ligament and help get rid of the inflammation. You can also bite down into the aligner without the Chewies to do the same thing.