From the Donkey Kong Country manual for the SNES, emphasis added:

> ... Donkey Kong had assigned Diddy to guard duty on this awful night,
> and he was not happy about his fate.
> 
> Donkey Kong's earlier pep talk kept creeping back into Diddy's mind.
> "OK, little buddy," Donkey had said in his patronizing voice. "As part
> of your hero training, you've got to stand guard tonight over my
> bananas... I'll relive you at midnight, so try and stay awake until
> then!"
> 
> Buddy? Yeah, right. Now he was alone [sic]Alone unless you counted the
> unknown threats which lurked behind every tree that he glimpsed during
> the lightning flashes. The Kremlings were out there, this much was
> certain. **They coveted Donkey Kong's banana stock-pile, the largest on
> the island, and probably in the world. A treasure in potassium and
> Vitamin A. The perfect food.** "Ahhh... delicious bananas..."

In spite of being reptiles, the Kremlings wanted DK's bananas because they are the "perfect food." This is probably from the perspective of the Kongs, its more likely that the Kremlings stole the bananas because DK valued them so much -- he stores them like money or treasure in a cave. Perishable bananas. In a big pile. You even collect them like the gold coins from that other popular platform game...

You know he's serious about these bananas because he vows to retrieve every single banana (even though in reality they would be inedible after a week or so):

> Donkey Kong stood there in stunned disbelief and hadn't heard most of
> what Cranky said. "Diddy... gone... My little buddy..." he murmured to
> himself.
> 
> Donkey Kong was suddenly filled with conviction. "The Kremlings will
> pay!" he raged. "I'll hunt them down through every corner of my
> island, until I have every last banana from my horde back!!"

Then Cranky Kong calls out the absurdity of retrieving stolen bananas as a video game plot:

> "Find your little buddy and retrieve a bunch of bananas?!" Cranky
> snorted. "What kind of game idea is that?! Where's the sreaming damsel
> in distress?!"

So they acknowledge the premiss is flimsy, but hot damn! The graphics and gameplay were awesome! So what if a bunch of reptiles stole the bananas? The point is we need retribution -- get those bananas (and Diddy Kong) back!