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."