All proccesors have onboard memory called cache. Cache is divided into levels, the first mainly being split into data and, something else, I forgot what it's called. Starting around mid 90's, proccesors for the home market got a second level of cache called L2 (first being L1). The L2 cache tends to be much larger than L1. This cache lets the proccesor access information it has just accessed again, preventing the need to take alot of clock cycles away to search in the main memory.
Cache matters on all machines regardless of use. Some programs it will help more than others because of constant calculations on basically the same thing. This apply's to games too.
Some one else could help me clear this up, as I'm not an expert on it.
Edit: generally for some applications, higher clock speeds can help more than large cache, but this varies alot (the more clock speed or more cache issue)
Mainly, more L2 cache means the proccesor can make more calculations instead of searching for information to make calculations on.
More cache gives better performance. That much is true. But at the same time, cache will not always yield the same amount of advantage. Some programs, like SuperPI, work a lot better with more cache, while others I think it was games perform better, but a bit more speed would negate the win.
I'd say it's too expansive to focus on L2 cache. I would buy a better graphics card if I was going for a gaming PC before considering getting more L2 cache.