Most packages provide a test suite. Running the test suite for a newly built package is generally a good idea as it can provide a nice sanity check that everything compiled correctly. A test suite that passes its set of checks usually proves that the package is functioning mostly as the developer intended. It does not, however, guarantee that the package is totally bug free.
Some test suites are more important than others. For example, the test suites for the core toolchain packages -- GCC, Binutils, and Glibc (the C library) -- are of the utmost importance due to their central positioning in a properly functioning system. But be warned, the test suites for GCC and Glibc can take a very long period of time to complete, especially on slower hardware.
As you progress through the book and encounter the build commands to run the various test suites, we'll guide you on the relative importance of the test suite in question so that you can decide for yourself whether to run it or not.