Like many other seeds and nuts, walnuts are incredibly rich in healthy nutrition.
According to USDA Nutrient Database, walnuts have a high concentration of fats (65%), with the highest proportion of poly-unsaturated ones, and a protein content of around 15%. (Ref. 1)
In fact, walnuts are probably one of the best studied nuts out there. Indeed, by now we know quite a lot about their health benefits.
For example, World's Healthiest Foods reports that the gamma-tocopherol form of vitamin E found in walnuts is more powerful than the alpha-tocopherol form commonly found in most other foods, especially in the sense of providing better protection against heart problems. Also, walnuts offer a very high content of valuable phyto-nutrients a lot of which are found on their skin. (Ref. 2)
So make sure you don't remove the skin but eat walnuts whole even if they may be slightly bitter. Quite often bitterness in many foods signifies that they possess some potent chemicals that normally fight free radicals in our bodies and may have many other functions.