cache is MEMORY, almost just like RAM. the rule of thumb is a piece of crap, and is outdated. cache here refers to system cache. and onboard usually means L2 (level 2). onboard means on the motherboard. L1 (level 1) cache has always been part of the processor.
Back in the days of the pentium, the L2 cache came in a card that was inserted pretty much like an expansion card, into a specialized socket just for cache RAM. The thing about cache is that, it is MUCH faster than system RAM, and MUCH more expensive. Cache is made of SRAM which is hard to make. Sometimes motherboards have the cache soldered on. In this case, the cache operates at the speed of the motherboard, usually 66MHz. And for Pentium systems, that had L2 cache on the motherboard, the size is usually 512KB. Though some motherboards supported as much as 1MB of cache.
You may have read that the Pentium II processors have the L2 cache in the cartridge, or how the newer processors have the L2 cache onchip. This cache operates FASTER. And since the cache is part of the processor as a whole, the motherboards for Pentium II systems don't have onboard cache. This is what your motherboard is, that is, it has no need, nor can it support, cache on itself as it is part of the processor. Socket 370 is just basically a different variety of processor connection for the latter type of processor i mentioned which has the cache on the chip.
enough of the background, why is cache important? well, cache is RAM.
you have several levels of storage of data on your computer. the slowest is your drives, HDD or CD\DVD-ROM or floppy. HDD is for permanent storage where your data and programs are stored. Then you have your system RAM, this is where your 128MB or whatnot comes in. when you access that data, or open that program for use, the data moves to the much faster system RAM.
Now, what about L1 or L2? In order for the computer to "process" data or execute a program, it has to go to the processor. Since system RAM is MUCH SLOWER than the processor, the processor has it's own L1 cache (which is RAM also remember, just MUCH faster than your system RAM) so it can store smaller amounts of data to be "processed" much faster due to the speeds over system RAM. With L2, well, the processor has a larger reservoir of data to draw from which is faster than system RAM. it is also important to know that data is exchanged constantly, so whatever you use, is whatever is stored in RAM, be it system, L1 or L2.