Monoglycerides and diglycerides are commonly added to food items to help them mix together properly. They are considered "lipids" or fats.
To be specific, a monoglyceride (mono meaning ONE) has one fatty acid chain. A diglyceride (di meaning TWO) has two.
As you might imagine, triglycerides have THREE fatty acid chains :)
Even though all three are types of fats, you really don't have to worry at all about two of them. Monoglycerides and Diglycerides are really not things to be concerned about. These two glycerides are not in 99% or more of the foods you eat. They are primarily used in bakery products, to help mixes remain together. They are present in such small quantities that the impact would be negligible. You probably burn them up with the effort of raising your fork to your mouth.
Triglycerides, on the other hand, are everywhere :) They in particular have been specifically targetted to reduce, to try to keep people healthy.
For example, when you measure your cholesterol levels, you usually test for LDL levels (bad cholesterol), HDL levels (good cholesterol) and triglycerides. These three numbers make up your total cholesterol count. Triglyceride counts should be below 150 mg/dl.
I have many, many articles that review the exact nature of LDL, HDL, how to measure your cholesterol, what healthy cholesterol levels are, and much more. Feel free to browse through my site and learn more about these topics!