L3 cache is a larger cache shared by all of the processors cores, while L1 and L2 are dedicated for each core. This varies by architecture of the processor, but its how it is with Phenom II and Athlon II(which lacks L3 cache).
Cache is general is like quick access memory for the processor to store data on while it processes data. My explanation is very crude and non technical, but it should give you an idea.
Phenom II, because of the L3 cache is faster per clock than Athlon II, but the performance gain varies greatly by task. You can already see in the image you linked, the Athlon II is clocked higher but that Phenom II has L3 cache and lower clock speed. The Athlon wins some tests that aren't cache sensitive while the Phenom wins some despite having the lower clock speed because the L3 cache helps it.