First, you want to check engine health, by looking at wear and contaminants. Various metals can help you identify any significantly wearing engine parts. Contaminants can tell you if you have any engine coolant leaking into the cylinders, and how well your engine air filter and oil filters are working. 

Second, you want to check your oil's health, to know if you can keep using it, need to change it, or learn what your appropriate oil change interval should be. The analysis will cover viscosity, TBN, fuel dilution, oxidation, nitration, soot, water, and coolant, as indicators for the oil's health. You can also check additive levels, like calcium, magnesium, phosphorus, and zinc.