Think of it as 8 processors all working at 2.0 Ghz.
If your applications are written to take full advantage of multi cores, they would run 8 times as fast by sharing the work load across all 8 cores. (this is theoretical. in the real world, you don't get the full 8X boost since applications tend to have to wait for operator input or HDD access.)
If your application is written to only run on one core, the one core would work at 2.0 G and the remaining cores are all idle, except that this processor also supports Turbo Boost if enabled so if your application only uses 1 core and the remaining are idle, the processor will boost to 2.4Ghz.
Most newer applications and OSes support mult core processing.
In windows you can view the processor cores in task manger under the performance tab and see which cores are working and how hard.