An idiom meaning extremely crowded or teeming with people (literally 'like washing potatoes'); used to describe places where people are jostling against one another.
初詣の神社は人が多く、境内は芋の子を洗うようだった。
The shrine for New Year's visits was so crowded that the precincts were like people washing potatoes (i.e., packed).
祭りの日は商店街が芋の子を洗うように混み合う。
On festival days the shopping street gets teeming with people.
朝の通勤電車は芋の子を洗うようで、乗るのも大変だ。
The morning commuter train is packed with people jostling each other, making it hard to get on.