Most of the time when people mention "benchmarking," they are referring to ways to compare one computer's performance against another's under the same software conditions. While this is useful to find the fastest RAM, quickest hard drive, or any other component that will give you the best bang for the buck, it can also be used to outline when the computer is running slower than expected.
Systems can run slower for a variety of reasons, including full hard drives, connected peripheral devices, large and complex user caches, or also from problems with file and file-system corruption. If your system does slow down, one way to see if an application or device is causing it is to use benchmarking suites to test the performance of the system as a whole as well as individual components to see if any notable slowdowns in performance occur when the system is running problematic software or running in another different configuration.
Some common benchmarks to use are GeekBench, XBench, and Cinebench to test the CPUs, GPUs, and RAM usage, but there are others such as Drive Genius and Disk Tools Pro that can run specialized benchmarks for hard-drive access, and still more for network health (those fun Java or Flash benchmarks for network speed). Some benchmarking suites are free, and others may require a license to unlock all options. It really does not matter what benchmarking software you have, as long as it will push the computer's capabilities.
Keep in mind that benchmarking for troubleshooting purposes is different than benchmarking for performance comparison between various systems. When troubleshooting you do not need to optimize the performance for the benchmarking suite. Instead, the goal is to get a baseline performance for your specific system with a given suite of benchmarks, and then test configuration changes against that same baseline to see if a notable or unexpected performance change develops when you know what the system's configuration change was.
Establish some baselines
The first step in benchmarking is to give yourself a baseline by running a benchmarking test or suite of tests on as bare of a system as possible. This means that when you first get your system set up, install a benchmarking utility and run the benchmarks a few times to get a baseline measurement. It may help do establish a few baselines for different possible hardware conditions as well, such as when on battery power and wall power for laptops, or when running an onboard/integrated graphics processor versus a discrete or dedicated GPU. You might also run them when booted into Safe Mode to see how the system performs with minimal drivers loaded.
Save the results of these runs as your baseline measurements, and write down how you ran the tests so you can replicate them at a later date. If you are extra diligent, you might consider running each baseline measurement a few times, and then averaging the results (or go even further and calculate standard errors and other fun statistics).
Testing the system
With a baseline measured, properly testing the system can sometimes be difficult, especially since many slow-downs are the result of contributions by multiple factors instead of one specific change. Nevertheless you can start by first running the benchmarks to see the overall performance change from the baseline, and then start testing various conditions by launching or quitting suspected applications and running the benchmarks each time to see if there is a significant jump in performance when a particular one is running. Do the same for when the system is on battery or in another configuration for which you have a baseline measurement.
Overall, benchmarking will likely not be a way you can quickly find problems with your system, but it can be used to show an overall slowdown when a specific change is made to the system and therefore help you determine where a problem is. I recommend using it in conjunction with Activity Monitor and other monitoring utilities to help outline what configurations and applications may be contributing to the system running slower.
While you can use benchmarks to test your system against itself, you can also compare the results to other people's results that have been posted online (usually at the benchmark's Web site); however, sometimes the results by average users can be misleading, especially if they do not describe the conditions for their results. I have seen some publically posted benchmarks that show a good 50 percent increase in performance over all other systems, only to find that the user forgot to mention his system was a dual-CPU system whereas the others were all single-CPU systems. While public benchmarking results can be fun to browse through, take them with a grain of salt.