Is teeth alignment painful?

Depends. There may be some level of discomfort with orthodontic therapy after each adjustment, usually manageable with over the counter medications if necessary. As the teeth move and the occlusion (bite) changes, the muscles controlling the opening and closing of the lower jaw sometimes may be tender.
Tolerable. Pain is subjective and everyone's pain threshold is slightly different. But what i tell my patients is that after you get your new set of clear aligners or after the dentist/orthodontist makes some adjustments, it's common to have some minor discomfort for the first 2 - 3 days afterwards but will be less painful after the first 3 days. Teeth alignment is done slowly to allow for less discomfort.