DNS - Domain Name Service. The DNS server basically translates a URL into the IP address of the server hosting the URL. If you type rtkamericas.topnetlive.com in your web browser, your computer needs to know what IP address corresponds to rtkamericas.topnetlive.com. Your computer contacts the DNS server, and "tells" it rtkamericas.topnetlive.com. The DNS server then "tells" your computer the IP address is 188.8.131.52. If you ping rtkamericas.topnetlive.com, the first line should be something that includes rtkamericas.topnetlive.com [184.108.40.206].
Domain Name - A domain name is what you usually type into the web browser when you want to view a page without the "www" part. This site's domain name is topconpositioning.com. Others you may be familiar with are google.com, yahoo.com...
Dynamic IP Address - The dynamic IP address is not really a type of IP address. The dynamic only relates to how an IP address is assigned. Your router hands out these IP addresses to computers every time they are rebooted. This means that every time your computer is rebooted, its IP address can change. You should have a static, not dynamic IP address if you are trying to do port forwarding. In a port forwarding configuration you must specify an IP address to forward the ports to.
Gateway - Usually this is your router. When you talk about your gateway, generally you are talking about the IP address assigned to a router. When you specify gateway in your TCP/IP properties you are entering the IP address of the router. If you enter your gateway into the browser bar, you get the web interface of the router.
NAT - Network Address Translation. When your router is using NAT, it is taking data from one Public IP address, and breaking that data into multiple private IP addresses. Data is sent to your network on a public IP address, from the internet. Using NAT your router then directs that data, to multiple internal private IP addresses. Nat basically breaks one IP into many. There is a problem with it though. When a computer on the internet wants to retrieve data from a computer on your network, your router can't figure out which internal computer to get the data from. This is where port forwarding comes in. Port forwarding tells your router which internal computer to get the data from when it sees data on certain ports.
NIC - Network Interface Card. This is a card in your computer that allows you to connect to routers/hubs/modems via ethernet. It's the thing your network cable plugs into.
Port Forwarding - Allowing your router to direct ports to a private IP address. The data on these ports is always incoming data, and always originates on an external public IP address.
Private(internal) IP Address - If you are using NAT, every computer on your network has one of these IP addresses. These IP addresses are provided by your router. Your entire network can see this IP address. Computers on the outside of your network can not, because your router "hides" private IP addresses.
Public(external) IP Address - Every computer/server that has a public IP address is directly connected to the internet. Usually DLS/cable routers are assigned a public IP address by the ISP they are connecting to.
Static IP Address - Static doesn't really refer to the type of IP address. It refers to how your computer obtains that IP address. Static IP addresses are hard coded into your computer by you, by hand. If you assign a computer on your network a static IP address, all the other computers on the network must have a static IP address.
Subnet Mask - The subnet mask is part of your IP address configuration. The subnet tells your computer which group of IP addresses you belong to and defines the range of possible addresses.
TCP/IP - This is the protocol your computer uses to communicate with other computers on the internet, and within your network. In windows this portion of your network properties, allows you to define an IP address, subnet mask, gateway, and DNS servers.