How does the Drupal LDAP module manage passwords?
This is all explained in the documentation and help text provided in the admin screens of the module.

Drupal supports multiple login sources. When a user logs in an entry for the type of login used for the person is stored in user_auth as an example.

By default LDAP does not store for example the AD password of the user within Drupal. It stores a dummy password and passes login info to LDAP from the login form upon a login attempt.

If you configure LDAP to sync drupal account information to and from Drupal then Drupal may store the password your LDAP accounts -- but this depends on how you've configured your LDAP service, and how you want the drupal ldap module to interact with it.