Bananas are simply a type of fruit. They appear in the episodes "Return to the Nightosphere," "Princess Monster Wife," and "Daddy's Little Monster," where they are excreted from the Demons' ears. They are smaller and more realistic than Banana Man and the Banana Guards, who are also bananas.
The Ice King uses a banana as his phone; somehow he is able to talk to people through one. He has a keychain on it.
Sometimes characters use some variation of "bananas" as another word for "crazy." In "Memory of a Memory," when he finds the Memory Core, Jake says, "It's banaynays down here!" In "Daddy's Little Monster," his video phone plays a recording of him saying, "So, this is the Nightosphere ... It looks banaynays." In "Princess Potluck," Finn tells Ice King to "stop acting nanners." Also, in "Mystery Dungeon," Jake says his "pie-dar's goin' nay-nays."
In "Orb," Finn, Jake and BMO sail back to Ooo from the island where the humans live. The boat they are on is stocked with a huge amount of bananas to sustain them. Nightmare Princess notices the bananas and decides to ask the trio through their dreams. When they figure out what she is doing, the group lets her take as many bananas as she wants. In thanks, she gives them a vial of "nightmare juice."