If your boss tells you not to test her patience, she means don't push her today, because she might just snap.
Surely you're familiar with vocabulary tests? In this case, someone is giving you difficult questions to see how much you know. Test more generally means "trial." If you test a soap on your skin, you use it on one small patch, to see if you'll have an allergic reaction. A drug test looks for the presence of drugs in your system. A difficult time in life is sometimes called "a test," because it's testing your strength to persevere.