Merriam-Webster is your friend...
success noun
suc·cess | \ sək-ˈses \
Definition of success
1a: degree or measure of succeeding
1b: favorable or desired outcome; also : the attainment of wealth, favor, or eminence
2: one that succeeds
Okay ... so that's a fairly broad objective definition, so it's fair to narrow it down with a little subjective re-definition.
I see 'success' as achieving or exceeding one's desired goals. If your goal is to finish a race, and you run the race to the end, then you have succeeded. If your goal was to win the race and you came in second, then you did not succeed. Simple.
It gets complicated when you start comparing your achievements someone else's achievements, or when you start measuring your success by some arbitrary standards set by your culture. Let's say you won that race I mentioned. Great, huh? But what if your time was a fraction of a second more than the time of last year's winner -- did you succeed? What if 'society' dictates that even though you won the race, the race itself somehow doesn't matter because it was 'only' a charity event, and not the Olympics -- did you succeed?
When I used to let 'society' (i.e., parents, relative, classmates, et cetera) dictate the standards of success, I was miserable. When I started setting my own standards of success (e.g., several smaller goals instead of one bigger goal), my outlook and attitude began to improve. With those improvements, my self-image improved, as well. With a progressively better self-image, I started setting progressively higher goals and succeeding at them! With each success, the failures mattered progressively less.
Advice? Start with small goals that you know you can attain, and master attaining those goals. Use what you've learned to take on bigger goals. Don't let lack of success stop you; keep trying and never give up until you succeed. If you find that success eludes you no matter how hard you try, set smaller goals and try again.
Never give up on yourself.