What is an example of an inorganic nutrient?

These are substances which are not carbon compounds. They include water, salt and other compounds which provide trace nutrients. We are unlikely to ingest anything as an element, except perhaps iron, which is converted to ions by the stomach acid and then absorbed. You need to be careful when describing inorganic nutrients. Whilst a biologist may refer to something like 'potassium in the diet' , if you are being accurate as a chemist you must remember that it will be a potassium compound that you ingest. (Potassium metal reacts violently with water.)

I believe they are things we need in our diet that are either simple compounds like water (H2O) or pure elements like iron.