There isn't really a good translation. 椀こ means small bowl (the こ is a diminutive) in Iwate dialect and there's a distinct style of eating soba there where you get 10+ small bowls of soba and can add all kinds of different toppings and ingredients, so you can really savor the range of tastes, but the portions are so small that all of them combined only make up roughly one regular sized bowl. And every time you empty a bowl, you stack them on top of each other (kind of like the shot glasses are stacked on top of each other in the picture).
Wanko soba is also often used in speed-eating and binge eating contests and all-you-can-eat restaurants/events. There a server stands by with trays full of small bowls and empies them continuously into your big bowl as it gets empty. It looks visually very impressive as dozens upon dozens of bowls stack up on the table, which is probably why it's so popular.