The technical term for post-exercise soreness is delayed-onset muscle soreness (DOMS).
DOMS usually peaks 48 to 72 hours after a workout, as your body really goes to work on the process to repair muscle fibers that were torn during exercise. There are varying degrees of pain depending on how much damage has been done (and other factors like genetics and how hydrated you are), but regularly experiencing an extreme level of soreness isn't something you should make a habit of.
Extreme soreness occurs AFTER you've done something your muscles aren't used to.
Fitness experts recommend changing up your exercise routines. So if you are used to something for a few weeks and change up to a different routine, working different muscle groups, expect some fatigue and soreness. When you’re body suddenly using muscles in new ways or engaging smaller muscles that your typical workouts rarely touch, you stress the muscles way more than they’re accustomed to or prepared for. Basically, extreme soreness can happen anytime you do something your muscles aren't familiar with—even if that's just going extra hard in a competitive bootcamp class.