Short story: pretty much anything that uses the processor will benefit from a larger L1 or L2 cache.
Long story:
Your cache is where your processor will look for data or instructions first. If the instruction/data is found in cache, it's much quicker to read it from there than memory. If it's not in your cache, the next spot it'll check is memory. If the data or instructions isn't in the memory either, then the last place to check is your harddrive or some other I/O device. When the data is found, depending on your processor's architecture, it'll probably be put into the cache (until it's replaced or discarded) or memory.
edit: a larger cache means more data can be stored there which increases the likelihood of finding the instruction on cache instead of memory/static storage.
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