Bananas have been shown to be used and obsessed over by the Kongs, being represented by Donkey Kong Junior's use of them against Mario in Donkey Kong Jr. and Junior's preferred item being a Banana in Super Mario Kart. With Junior being the first shown to establish the Kong's love for the fruit, it's likely he also had the concept of collecting them into a constantly growing hoard, a tradition/legacy continued by his son prior to Donkey Kong Country as a tribute to him.
King K. Rool stole the Bananas to starve the Kongs to death in Donkey Kong Country. Donkey and Diddy Kong battled through all of the bosses and Kremlings that raided Donkey Kong Island in order to retrieve their precious hoard. They appear to win a giant Banana for every boss they defeat, and the boss arenas themselves appear to be comprised of some of DK and Diddy's stolen Bananas (as if K. Rool ordered all of the bosses to steal DK and Diddy's Bananas with him), though the game will not show the hoard gaining any size at all until K. Rool is taken down.
If the Kongs did not defeat K. Rool and they try to visit their hoard here, they will see their empty hoard, and do their "bonus lose" animation. However, when they finish the game, they will see their hoard full and do their "bonus win" animation.
The Banana Hoard does not make a physical re-appearance in the handheld sequel to Donkey Kong Country, though it was stolen again by K. Rool after DK and Cranky made a bet before the events of the game, where DK and Diddy reclaim them on an 8-bit system.
The Banana Hoard does not make a visual re-appearance in the sequel to Donkey Kong Country, though it does have an importance in the story.
In this game, K. Rool kidnaps DK and demands the hoard as ransom. Diddy refuses, explaining how hard he and DK worked to recover it in the last two games and how crazy DK would be if he lost his hoard again. Diddy and Dixie set out on a quest to rescue DK in order to protect their Bananas.
The Tikis steal all of the Bananas once again in Donkey Kong Country Returns and Donkey Kong and Diddy Kongmust chase after the Tikis to get their Bananas back. Like in Donkey Kong Country, when the Kongs enter the Banana Hoard, they will find it empty unless if they complete the game. In the factory levels, the Bananas are shown being used to create more Tikis.
It is revealed during the factory levels and the final boss fight with Tiki Tong that DK and Diddy's Banana Hoard are Magical and consuming even a small amount can grant that person a massive power boost in raw strength and Magical capability (as evidenced by the dangerous Tiki Tong's expanding size and hands as well as giving life to ordinary wood, hence the birth of new Tikis), providing another reason for why DK and Diddy's enemies are always trying to take them.
Later in the game and the sequel Donkey Kong Country: Tropical Freeze other Bananas Magical in nature are shown to have sentience like having eyes and wings, they are capable of flight and producing many new Bananas. Collecting 100 bananas are worth an Extra Life Balloon, drinking Banana Juice grants invincibility for 5 hits, Funky Kong's idle animation shows him tapping into their raw potential by waxing his skimboard with a banana peel, letting it absorb the fruit's Magical juices and explaining his skimboard's ability to hover, glide, and fly.
There are hints to a possible Banana God (aside from the Banana Queen a guardian deity that rules over the Banana Birds in Donkey Kong Country 3: Dixie Kong's Double Trouble! above the clouds), Donkey Kong Country Returns and Donkey Kong Country: Tropical Freeze showcase statues, temples, and illustrations depicting bananas with faces on them and Kong-like apes worshiping bananas. The shiny Banana (found in the Golden Temple) that Donkey and Diddy eat transports them to a world above the clouds.