These "stones" can cause pain, ear infections, and particuarly bad breath. That's why they should be removed.
If you press carefully with the bottom of a toothbrush or a cotton swab then they often fall out on their own. They can sometimes be "washed out" with a dental water jet. No need to panic if you accidentally swallow them.
If you suspect you have tonsil stones, and you don't trust yourself to "push them out," or it's painful, then it's worth visiting a nose / ear specialist or the dentist. This can remove the stones easily and effectively and give you advice on how to prevent them next time.
You can see a video on how to remove them here: