Assure is about facts. Someone is worried and you confirm some information because you KNOW.
I can assure you that we clean the rooms every day.
- I know that we clean the rooms every day.
Reassure is more about emotions. Someone is worried and you just want them to stop worrying.
He reassured me that his parents would like me.
- he THINKS his parents will like me, he may not be 100% sure but he wants me to stop worrying about meeting them.