The IP address you specified is a private IP address, which means it isn't actually used on the Internet.
When you setup TightVNC on your computer, to access the computer from WITHIN your network, you would use the client to connect to that computer with that IP address and port, and it would work fine. However, if you plan to remote into your computer from anywhere else on the Internet, you would then need to instead provide the client with your home's public IP address (provided by the ISP) and port number. You would then just tell your router to forward requests for that port (5800) that are coming from the Internet to the internal IP address of that computer (192.168.1.101) and to that specific port.
Yes, there are a lot of routers that provide the 192.168.x.y IP address range to clients, but because that IP address range is private and not used on the Internet, Internet routers don't care for them and "ignore" their use, so you have to instead provide the public IP address so Internet routers know how to route the request to your house. At your house's router, your router knows which internal computer to route the request to based on the port forwarding you'll have setup.
ok thanks, I appreciate the responds. It's an odd story of how I got confused.
I was helping my friend out setting up VNC and I thought to put his private addy in from my house (which of course didn't work). Then after a while, my friend asked how does the packet know which computer to send it to if the IP addy are the same. Since I was using his private addy, I confused the heck out of myself.
Well after a while I realized I had to use his public addy and it all hit me at once. And after skimming through your explanation, it all made sense again, lol.
Well thanks again KiLLaBeE, I appreciate you taking your time to respond to my post.