I have a webservice (web.py+cx_Oracle) and now I will call it with localhost:8080/...!
On the local pc it is working. But after installation on a second pc for testing purposes it is not working there. All versions are the same!
On the second pc the browser is asking for a username and password from XDB. What is XDB and why is he asking only on the second pc?
On the first pc everything works fine and he is not asking for username and password...Can someone explain to me what is going on?
XDB is an Oracle database component. It would appear that on your first PC, you're able to automatically log on to the database which is why you're not prompted. However, the second PC isn't able to, so you're prompted. 
Compare using SQL*Plus (or other oracle client) from your two PCs & configure PC #2 so that it won't require a login (or modify your cx_oracle connect() call to provide the correct connection parameters (user, password, dsn, etc.)
Asking for username and password from XDB