To put it differently, hashing without salting lets an attacker crack the entire database at once. Try a password, see if the hash is in the database, repeat.

With salts, the attacker can only attack a single user at a time. Try a password with one user's salt, see if the hash is in the database, try the next user's salt, see if that hash is in the database, repeat.

Salts don't need to be secret to work.