The word dilemma origninates from Ancient Greek and Latin, meaning "a difficult choice or problem."  It's derived from the Greek word "δίλημμα" (dílēmma), which translates to "double proposition."  This Greek word is a combination of "δι-", meaning "two" or "double," and "λῆμμα", meaning "premise" or proposition".  Initially, it was a term in logic, referring to a specific type of argument with two conditional statements, but it evolved to describe any situation involving a difficult choice between equally undesirable options. 

The word "dilemma" first appeared in English in the early 16th century, around 1523.  By the end of the 16th century, the word's meaning began to broaden, encompassing any difficult choice of situation.  Today, "dilemma" is commonly used to describe a situation where a difficult choice must be made, even if the options are not necessarily equally undesirable.

Example of "dilemma" in a sentence:  
"Jonathan was faced with the dilemma of whether or not to return home after the argument." 
"Emily was faced with the dilemma of whether or not to report her colleague for embezzling money from the company." 
"Some people often face the dilemma of feeding themselves or their cattle during times of great hardship."  
"The dilemma, like all ethical dilemmas, arose by virtue of a conflict between values."  
"He made an attempt to resolve the long-standing dilemma." 
"The new school rules have put counselors in a terrible dilemma." 
"Prodding Martha to talk out her dilemma helped, didn't it?" 
"After overcoming that dilemma, I think our friendship is stronger."

Just the facts:

DILEMMA Definition & Meaning - Merriam-Webster

DILEMMA Synonyms: 48 Similar and Opposite Words | Merriam-Webster Thesaurus

Websters 1828 - Webster's Dictionary 1828 - Dilemma