The L2 and L3 cache are for holding data that is to be used by the cpu next. For higher performance you do need higher clock speeds and the more cores the more the cpu can proccess at once and the more programs and tasks the cpu can do at the same time. Higher clock speeds means how fast it can go also.
Cache is basically just high speed RAM built directly on the CPU. An old rule of thumb:
*)If data is in the L1 cache, the CPU can get to it in about 1-2 clock cycles
*)If data is in the L2 cache, the CPU can get to it in about 10-20 clock cycles
*)If data is in the L3 cache, the CPU can get to it in about 50-80 clock cycles
*)If data is in RAM, the CPU can get to it in about 80-100 clock cycles
*)If data is on the HDD, the CPU can get to it in about 100,000 clock cycles [see why more RAM helps performance?]
Numbers vary a bit by processor architecture, but each level of cache down gets larger, but also takes slightly longer to access. As you can see, on a system with enough RAM to avoid a Page Fault [needing to go to the HDD to load data into RAM], the L3 cache has very limited performance benefits. Hence why some argue that the space the L3 cache occupies on the CPU die would be better used for some other purpose.