What is the root of word dilemma?

The root of the word "dilemma" is the Greek word "dīlēmma", which literally means "double proposition" or "double choice". It is formed from the prefix "di-" meaning "two" and the word "lēmma" meaning "proposition" or "premise".

So, a dilemma is a situation where you are faced with two difficult choices, each with its own set of advantages and disadvantages.