We do not know how exactly Facebook manages user passwords, however, we can imagine this scenario:
A new user logs into his Facebook account using the password: Password1. It is likely that, immediately, Facebook generates similar passwords such as: Passw0rd1. pAssword2, Passmord1 ...etc.
Facebook then stores their respective hashes (which are different, of course) so that if a user user types his password (after reset), the hash of the new password is compared to all these stored hashes: Facebook can tell you then if your new password is similar to the previous one or not.
EDIT:
Following @Philipp comment saying Facebook does not hash passwords, I want to share this information that I quoted from the official Facebook documentation (Keeping Passwords Secure):
We hash each password using our internal password hashing algorithm
and the unique salt for that person. Since Facebook stores passwords
securely as hashes, we can't simply compare a password directly to the
database. We need to hash it first and compare the hashes.
password, the HTML page on your machine replaces some letters, hashes them and send the hashes. I think you should ask someone who is professional at HTML programming :/ – Eibo Oct 04 '15 at 13:02