Most people go the other way round: Banana for K [= potassium]; believing that bananas are a rich source of potassium and also that most of us are chronically short of the stuff. We need nearly 5g of potassium every day [advised intake AI = 4,700mg/day] to keep up with the amount we are peeing out. The balance between potassium and sodium is critical to correct muscle and nerve function, and the kidneys work hard to claw these ions back from the flow but inevitably some dribbles away and must be replaced.
The why bananas could be due to either of two attributes: the potassium or the ethylene (C2H4).
Potassium is a silly reason to use bananas for this reason because there are an alphabet of fruit and vegetables that are a richer source of potassium than bananas: avocados, beans, chard . . . Please use the avocadoes because they are virtually indestructible in the compost pile - I sift out their stones and skin whenever I process our compost heaps.
Ethylene is a gas, one of the really simple beginners building blocks for organic chemistry. It can be polymerised in the presence of a catalyst - often Titanium III chloride - and then extruded as sheets or threads to make polythene. We get through a helluva lot of the stuff each year - around 100 million tonnes according to the industry. But long before plastics, ethylene was being used by plants as a hormone /pheromone to promote flowering and ripening of fruit. Bananas and other fruit give off ethylene as they ripen which brings on the process in surrounding fruit; which creates a cascade effect. This coordinated action may confer some evolutionary advantage - overwhelming potential predators with a glut, maybe? CO2 contrariwise slows down fruit ripening and this gas is used on banana boats (as well as chillin') to allow the fruit to arrive still green in Waterford several weeks after picking.
Why orchids is another conundrum to me. I can find lots of assertions that the banana - orchid axis is A Good Thing but very little evidence that the associative effects are any better than random. I'm going with my essay on the etymology of the word orchid [όρχις = orchis is the Greek for testicle] and suggest that any banana-benefit peculiar to orchids is a load of bollix.