>>Do I understand correctly (sorry for many questions) that the username to a PC is the username your code needs to connect to the AD?

For LDAP It's not actually a username, it's a "Distinguished Name" (DN) with other stuff included. Check out the example in the code with username and "example.com" domain components, and it's worth visiting that site for some more examples of dn involving Organizational Units (groups) and usernames.

The code attempts a LDAP "bind" with the DN and password. Success means credentials are valid.

>>In this case, if this is correct, I simply need to find out one of my customers username and password and test your code.

You'll also need their domain components, so if it's newexample.com you might have for your DN uid=myusername,dc=newexample,dc=com

(Yes the dc is wierd, but that's what LDAP expects.)

>>So far, as I wrote before, my code connects to the AD by only using the username. I am a little confused as to how my .NET app can connect to the AD without a password.

Maybe you're connecting as the currently logged-in user? Is it using LogonUser or LDAP behind the scenes? What parameters?