User authentication handled by a web service
Remote authentication can range from moderately complex to major complex.  

In general, you will need Drupal users that match your external DB users.  Drupal security and coding is tied to this.  The easiest way is to create users that match your remote DB and then only do authentication.

How you syncing the remote to the local can quickly add complexity.

Other things you will need to deal with are overriding the password reset functionality.  Changing it in Drupal will not change it in your remote DB.

Some reference material / modules to look at:

Authentication API (incomplete)

The LDAP Project - A full featured implementation with dynamic provisioning (creates local Drupal id's if user authenticated) and other stuff.

The External Auth Module - Just ran across this.  May or may not be applicable.