Answer:
This poem, as stated in the title, is about not quitting.
It uses an informal dictation, as if speaking to a friend- as if giving you advice. It takes on the air that the author has been there, done that.
He speaks of feeling as if everything is awful- "When the road you're trudging seems all uphill," he states in the poem.
The word trudging suggests that the walk is not an easy one and when combined with the word uphill, suggests that the path they are taking is hard.
The poem also hints at depression- "And you want to smile, but you have to sigh".
This is suggesting that the narrator is thinking of giving up, because life is so gloomy.
He tells us "When he might have won had he stuck it out", most likely meaning that the narrator lost his fight, but is advising you not to do the same.
The connotation is a feeling of hope, while the deeper meaning is to never give up.
I hope this help! ^^