Bananas are a good quick source of energy/healthy sugar (hence why they're suggested for diabetics with low blood sugar), so it'd make sense to offer one to an athlete as a snack.
About the banana thing: in France, we say ‘I have the banana’ when we’re happy and energetic. To ‘give someone the banana’ means to give them positive energy basically (and yea THE banana not just any banana)
Dunno if it applies here tho lmao