Merriam-Webster Dictionary and the Oxford Advanced Learner's Dictionary both define failure as;
'Lack of success.'
The latter adds that failure is;
'an unsuccessful person or thing.'
Life is best taught by experiences, not by textbook definitions and failure being an intrinsic part of life is also best defined by experience.
We'll examine how those that have experienced failure defines it.
“Failure doesn’t mean you’re a failure; it just means you haven’t succeeded yet.” - Robert Schuller
“Failure is only the opportunity to begin again more intelligently.”- Henry Ford
"Never confuse a single defeat with final defeat.” – F. Scott Fitzgerald
"You always pass failure on your way to success.” – Mickey Rooney.
And my best of them all;
"Failure is an event, never a person.” – William D. Brown.
Failure is that sure stony and stormy path that leads to the beautiful destination.
Cheers