Meaning #1
The names of 5 gods in Dragonball Z. Four of them are charged with taking care of one quadrant of the mortal plane, while the fifth is in charge of them and the spirit world. The one known as King Kai is actually North Kai, who has counterparts in South Kai, East Kai, and West Kai. They apparently never show up in Toriyama's manga, but they do show up in the anime shortly after the Cell Saga.
The fifth Kai is called the Grand Kai, and is (supposedly) the most powerful being in the universe. But by the time Goku meets him (after his death during the Cell Games), he is already more powerful than the Grand Kai.
Just to confuse matters, there are 5 more gods, each more powerful than tha Grand Kai, called Kaioshin. All but one was killed millenia ago by Majin Buu (which one is quite uncertain). In any case, the surviving one is called the Supreme Kai (not Kaioshin) in the US anime releases, leading to confused statements like "Even the Kai(0) are not allowed into the sacred land of the Kai(1)" where (0) refers to the actual Kai, and (1) refers to the Kaioshin (the Supreme Kai and his dead pals).
Meaning #2
KAI is the name of a commercial compiler vendor. Actually, it's an abbreviation of Kuck & Associates, but it refered to pretty much exclusively as KAI. The are located in Champaign, Illinois.
For many years, KAI C++ was basically the champion of C++ compilers. It was incredibly portable, running on Windows NT, Linux, Tru64, IRIX, Solaris, and even Cray and Hitachi supercomputers. In addition, it was much further along in terms of standards compliance than other compilers (commercial or free) at the time. Lastly, it could generate could that would blow away what GCC (or most other compilers of the time) could do. Some informal testing by myself in 1999 showed KAI C++ to generate code that ran about 2 to 3 times as fast as egcs. Even today, KAI C++ can compete with the most recent GCC releases in terms of code optimization.
KAI C++ is based on software by EDG (aka Edison Design Group). They basically sell a C/C++ front end, to which various customers can add their own optimizations and support for specific CPUs. Other compilers based on EDG include Compaq's C++ compiler, and (I think) SGI's as well.
KAI added lots of cool optimizations onto EDG's front end, and for a backend, they did a clever trick. They convert the input file (C or C++) into highly optimized C code, and then give this code to the native compiler to actually convert into object code. The first C++ complier, Cfront, also did this (though it didn't have the optimizations KAI C++ has, of course), but most compilers now convert C++ directly into assembly without the intermediate step. This is mostly because Stroustrup probably didn't want to write a complete C compiler, which you would have to, since C++ is a strict superset of ISO C. But once you've got a C compiler working, adding support for C++ is fairly simple.
In addition to their C/C++ complier, they sold various performance analysis tools and an OpenMP compiler for C, C++, and Fortran.
Their support was also about the best I've ever seen. I found 3 or 4 bugs in the optimizer a few years ago, and each time they were fixed within a day or two of talking to support.
In April 2000, KAI was bought by Intel. Since then, they have been essentially shut down - no new copies of any KAI products are being sold, and support will only be available for existing installations for a few more years. Intel recommmends switching over to their line of C/C++/Fortran compilers, and while their stuff is quite decent, and produces very fast code on x86 systems, it leaves KAI users on non-x86 systems out in the cold. I presume that they bought the company specifically because they wanted help on their own compilers, especially since IA-64 compilers need to be very "smart" to take full advantage of the exceedingly complex VLIW instruction set.