Network Connections is where you configure TCPIP Properties that will be needed if you attempt to network with another device by trying to send an email or surfing the Internet. Once you get your home gateway configured, you will want to check a few things on the Properties of your NIC to complete your home network access. Transmission Control Protocol\Internet Protocol, or TCP\IP, is where you configure settings for network connectivity and the primary protocol stack (a group of protocols lumped together for certain usage) for communication across the Internet!
After your home gateway is configured, you will want to check your TCPIP settings to ensure everything is in working order - these are the settings that allow your computer to communicate to the home gateway for Internet access. 
There are a few ways to get to these settings such as 'right' click the network icon in the system tray and select 'Open Network Connections' from the pop-up list.
Or you could use your mouse to click on Start, then Control Panel. There should be an icon under the Control Panel that is named Network Connections. However you get there, you will need to navigate to the Properties of either your Local Area Connection if your gateway is wired, or Wireless Network Connection if you are wireless. Browse to the TCP/IP Properties and select Properties right beneath it. If you have never messed with them, the settings should still be at Default values, which is fine in most cases. Ultimately, you will want your network card (or NIC) to 'Obtain an IP Address Automatically' via DHCP (Dynamic Host Configuration Protocol) as well as 'Obtain DNS Server Address Automatically'. 
This will allow your computer to 'pull an IP address' from your home gateway which you have already configured to act as a DHCP server!
