After the installation of the .NET Framework you will find the ASPNET account on the local computer. If you start a ASP.NET web application this account will be used by the ASP.NET worker process (aspnet_wp.exe). For security reason the user has only some privileges, of course, no network access.
If you want to access data on a network drive you can change the userName in the machine.config's processModel section. You can enter there a domain user and his password, but this is not very secure!!
A easier way is to create a copy of the local ASPNET account and change the password. After this create a copy of the server's ASPNET account and specify the same password. After you have changed the userName in the machine.config you can access the network.
With Microsoft .NET Framework version 1.1 you can specify the password encrypted. Then I hope there is no more security problem with the ASP NET user account...!