行雲流水、in Japanese represented as "こううんりゅうすい" has the characters for "going" or "moving", "clouds," "flow" and water, read from up to down with the right column first. More or less literally meaning "clouds move, water flows" it's taken as idiomatic as "go with the flow" or "going with the tide" according to on-line translations, more or less, but that's I think a bit superficial. Oh, and the Chinese version of the translation of 行雲流水 has "fill the gap" or something like that.
Also I think Wikipedia's entry here is a bit superficial and contradictory (as I'll show in in a bit):
Unsui (Japanese: 雲水), or kōun ryūsui (行雲流水) in full, is a term specific to Zen Buddhism which denotes a postulant awaiting acceptance into a monastery or anovice monk who has undertaken Zen training. Sometimes they will travel from monastery to monastery (angya) on a pilgrimage to find the appropriate Zen master to study with.
The term unsui, which literally translates as "cloud, water" comes from a Chinesepoem which reads, "To drift like clouds and flow like water." Helen J. Baroni writes, "The term can be applied more broadly for any practitioner of Zen, since followers of Zen attempt to move freely through life, without the constraints and limitations ofattachment, like free-floating clouds or flowing water." According to author James Ishmael Ford, "In Japan, one receives unsui ordination at the beginning of formal ordained practice, and this is often perceived as 'novice ordination.'"
Then again, there's this Chinese tea ceremony thing that uses the same term. Which is why I think there's a bit of contradiction there. I realize I might be more than slightly out of my depth here as I try to find the original poem from which 行雲流水 comes. That is to say, although I think I can find the original poem from which 行雲流水 comes, my knowledge of Chinese is pitifully poor to the point where there's no reasonable way I could put 行雲流水 in proper Chinese context at this point. Maybe in 10 years...
The version of 行雲流水 that comes down to us as in Wikipedia is like a replica of a replica of a replica of something that was in a Chinese poem once.
But that's only part of why I think the conventional "explanations" of 行雲流水 are a bit superficial...
First of all, 行雲流水 is meant to be put into 書道 (or 書法 if you prefer the Chinese term). 行雲流水 begs to be expressed as 書道. See, unlike, say, Magritte's famous not-a-pipe picture, or the Zen expression "a picture of a rice cake does not satisfy hunger," 行雲流水 as 書道 is almost perfectly non-dually expressing flow without flowing, if executed even minimally competently. Or to put it another way, if you want to do 行雲流水 minimally competently, you have to express 行雲流水 in 行雲流水 .
I would love to have help finding the poem which gave fame to 行雲流水, and understand it. But in the mean time, realize this is a bigger deal than you'll get in Wikipedia.