Tunneling
Tunneling is a method used to connect computer systems that are in different locations as if they were on the same local network. This works by encrypting all of the data that would normally travel over a LAN into single data stream, creating a secure channel, or "tunnel," that is not accessible to the general Internet.
Xlink Kai uses this method in much the same way that a corporate virtual private network (VPN, a term that describes how certain tunneling protocols work) uses tunneling to allow access to network resources that would not normally be usable over the Internet. Xlink Kai uses the tunnel to transmit system link data that isn't meant to be routed over the Internet. Additionally, while most VPN systems require that ports ("channels" that specific types of data are sent over) be opened for them to work, Xlink Kai works without any extra configuration.
Xbox Voice Chat
Voice chat on the Xbox usually runs over the Internet, rather than system link. Most games do not support voice chat over system link. It's reasonable to suppose that the designers expected gaming over system link to be done within hearing distance of the other console. Using Xlink Kai, these games will not support the use of Xbox voice chat. However, this can be worked around by running a third-party voice chat program on a personal computer. A small number of games do support voice chat over system link, and these will work as expected.
Xlink Kai does support voice chat on an Xbox running XBox Media Center (XBMC). Using this method, voice chat will work while playing any game. However, this requires modifying an Xbox and installing third-party software, which is not a trivial process. This can result in the modded Xbox being banned from Xbox Live. It also will work only when all the machines joining the game are similarly modified.
Lega Considerations
Xlink Kai is a wonderful tool for gaming with friends on the original Xbox. Unfortunately, Microsoft treats it as a piracy tool, as Xlink Kai has the ability to allow unauthorized copies of games to be played online. It also avoids the monthly fees for Xbox Live. This results in Xlink Kai and similar software being labeled as a circumvention device under the Digital Millenium Copyright Act (DMCA).