The word "odyssey" comes from Ancient Greek Odysseia, meaning "the story of Odysseus".  Odysseus was the hero of Homer's epic poem The Odyssey, which recounts his ten-year journey home after the Trojan War. The English word "odyssey" was adopted around 1600 from the poem's title, and its figurative sense of a "long, adventurous journey" emerged later, by 1889. 

According to the Oxford English Dictionary (OED), the first recorded use of the noun "odyssey" (with a lowercase 'o') used in English referring to a long, adventurous journey was in 1886, appearing in Robert Louis Stevenson's novel Kidnapped.  Before this, the term was primarily used to refer to the ancient Greek epic poem by Homer.  However, the word "Odyssey" (with an upper case 'O') was first used to describe Homer's epic poem in a translated English test around the early 17th century,  with George Chapman producing the first complete English translation of the epic in 1614–1615. 

Examples of "odyssey" used in a sentence: 
"The story is about the emotional odyssey experienced by a teenage girl." 
"Once free of the camp, the greatest threats of their odyssey were hunger and men."
"This book is about his odyssey to walk the entire length of the chasm with a friend."
"To reach the location on the edge of town is an odyssey."
"My twenty-year odyssey in the army allowed me to visit eighteen countries." 
"After enduring a messy divorce, Jill left the country and embarked on an emotional odyssey to rediscover herself." 

Just the facts:

ODYSSEY Definition & Meaning - Merriam-Webster

ODYSSEY Synonyms: 37 Similar Words | Merriam-Webster Thesaurus