VNC - virtual network computing - is a method of access the desktop of one computer on another computer using a network connection. While the original VNC worked well over local networks, the amount of data to be transferred could seriously impact performance over slower connections. This even applies to current fast ADSL and cable connections because of the limited uplink speed form the computer you are accessing. TightVNC takes the standard VNC protocols and adds compression for faster use over slower networks.
Having remote access to another computer has several uses such accessing your home computer from work (ask permission before trying the other way round), remote administration or fault fixing. TightVNC works with standard VNC too, it enables the compression of the computer it is talking to only uses standard VNC, and you can use that slower connection to install TightVNC on the emote computer before reconnecting if you wish. VNC is a completely open and free protocol, so it is implemented on all popular operating systems, and the same is true of TightVNC.