If you just want a quick and easy way to resolve a hostname to an IP address you can usually just use a command line tool like ping. For example, open a command prompt and type something like this:
>ping newgrounds.com
Pinging newgrounds.com [198.41.187.234] with 32 bytes of data:
Reply from 198.41.187.234: bytes=32 time=11ms TTL=56
Reply from 198.41.187.234: bytes=32 time=14ms TTL=56
Reply from 198.41.187.234: bytes=32 time=11ms TTL=56
Reply from 198.41.187.234: bytes=32 time=10ms TTL=56
Ping statistics for 198.41.187.234:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 10ms, Maximum = 14ms, Average = 11ms
Ping is a tool that lets you measure latency (lag) between yourself and another machine. By pinging a hostname or IP address, your computer sends a packet or series of packets to that location. It counts the amount of time it takes for the packet to come back to you, which gives you an idea of either how far away it is, how much load the server is under, or how bad your own connection is. The target then sends them back to you. It works similarly to how radar and sonar work.
If you just want to resolve the hostname to IP and don't care about ping times, you can use a tool like nslookup instead:
>nslookup newgrounds.com
Server: UnKnown
Address: 192.168.1.1
Non-authoritative answer:
Name: newgrounds.com
Addresses: 198.41.187.234
198.41.188.234
Note: The examples I just gave you are for Windows. Similar commands exist on *Nix but they tend to produce slightly different looking output. All-in-all though commands like ping and nslookup are considered the "bread and butter" of basic networking tools.
If you're genuinely interested in learning how networking works I suggest reading some of these first.
http://en.wikipedia.org/wiki/Internet_Protocol
http://en.wikipedia.org/wiki/Internet_protocol_suite
http://en.wikipedia.org/wiki/Transmission_Control_Protocol
http://en.wikipedia.org/wiki/User_Datagram_Protocol
Someone already said this but I'll just recap... That page is hosted on Newgrounds. The IP address would be for a Newgrounds server.
Newgrounds doesn't actually operate on a single server anymore (at least I wouldn't think it does) and likely has a farm of them with load balancing, etc. The newgrounds.com TLD (top-level domain) is probably mapped with a load-balancing DNS so depending on where you're connecting from and which servers are under the least load, that is the server IP that it will be mapped to. Newgrounds also has auxiliary servers that are provisioned specifically for things like serving files (ngfiles.com) which don't actually serve HTML. This falls in line with a computer science principle known as "separation of concern."
More on that here:
http://en.wikipedia.org/wiki/Separation_of_concerns
If you're really interested in all of this stuff I can probably PM you a more comprehensive list of articles. You should probably visit your local library and see if they have any good books you can read. Also, if there are any kind of networking classes at your school, you should consider taking them.