I used netstat to see what is happening with network connections, and I see this weird ip address somehow listed together with PID 4 "NT Kernel & System", whatever that might be. Netstat describes it as a "local address" and there is no "foreign address" involved (btw, what are local and foreign addresses anyway?) In the column to the right there is neither "listening" nor "established" record, so no record at all there.
By "Local," netstat is referring to IP addresses that are bound locally to your system. By the same token, "Foreign" means IP addresses that are not bound locally to your system.
Your IP address, 10.1.1.130, is also a Private IP address. On a side-note, RFC 1918 specifies which IP addresses are reserved for Private use (10.1.1.130 is a Private IP address):
RFC 1918 - Address Allocation for Private Internets
10.1.1.130 is probably your local IP address. Although it is possible to have multiple IP addresses bound locally to one of your system's interfaces, most users only ever get one IPv4 address (and lately they may also get an IPv6 address too as the internet slowly transitions over to IPv6).
"Listening" means that a daemon (or Service) is actively waiting for connections to the identified TCP port. A good example of a daemon would be Apache HTTPd, which usually listens for new connections on TCP port 80 for HTTP requests (and 443 for HTTPS requests), then services them accordingly (sending web pages or error codes as per the protocol, depending on what was requested).
"Established" means that an active connection is being serviced.
Local and foreign addresses relate to IP address ranges. Local address or private is an IP within the specified range for internal netowrking only, its not routable on the open public/foreign internet. Typically a private/local IP will be used on a home NAT network. Wikipedia - Private Network