In the Tao Te Ching water stands for effectiveness without status. Chapter 8 praises it for taking the low place everyone avoids, chapter 78 uses it to argue that the soft overcomes the hard, and chapter 43 explains why: what has no fixed shape enters where there is no opening.
Chapter 8: conduct, not gentleness
The highest excellence is like (that of) water. The excellence of water appears in its benefiting all things, and in its occupying, without striving (to the contrary), the low place which all men dislike. Hence (its way) is near to (that of) the Tao.
The claim is not that water is gentle. It is that water goes where status is lowest, and that this — not softness — is what puts it near the Tao. Benefiting all things and occupying the low place which all men dislike are named in the same breath, as one behaviour rather than two.
The chapter closes by naming the consequence: when one with the highest excellence does not wrangle about his low position, no one finds fault with him. The reward for not competing is not victory. It is the absence of an opponent.
Chapter 78: a claim about force
There is nothing in the world more soft and weak than water, and yet for attacking things that are firm and strong there is nothing that can take precedence of it;--for there is nothing (so effectual) for which it can be changed.
Every one in the world knows that the soft overcomes the hard, and the weak the strong, but no one is able to carry it out in practice.
This is not encouragement. It is an observation followed by a complaint: everyone in the world knows it, and no one is able to carry it out in practice. The book is not telling you that softness wins — it is telling you that you already knew, and that knowing has not been enough.
That complaint is unusual here. The Tao Te Ching rarely addresses the reader's failure so directly, which suggests the author expected agreement and did not expect it to change anything.
Chapter 78 then closes with a quotation inside the quotation — the author citing an older saying, which is rare in the book and worth noticing.
Therefore a sage has said, 'He who accepts his state's reproach, Is hailed therefore its altars' lord; To him who bears men's direful woes They all the name of King accord.'
He who accepts his state's reproach is hailed its altars' lord. The low place again, now stated as a rule of succession: authority lands on whoever absorbs what nobody else will carry. And the closing line names the difficulty honestly — words that are strictly true seem to be paradoxical. The book knows this sounds like nonsense and says so.
Chapter 43: the mechanism
The softest thing in the world dashes against and overcomes the hardest; that which has no (substantial) existence enters where there is no crevice. I know hereby what advantage belongs to doing nothing (with a purpose).
That which has no substantial existence enters where there is no crevice. The argument is about access, not strength. Hardness cannot get in; the thing with no fixed shape is already inside. Water is the example, but the claim is general — and it is chapter 8's point about status, arriving from the other side.
Chapter 66: the argument applied to power
Chapter 8 said the low place is where excellence goes. Chapter 66 turns that into a claim about how authority actually works, and it is the most concrete passage of the four.
That whereby the rivers and seas are able to receive the homage and tribute of all the valley streams, is their skill in being lower than they;--it is thus that they are the kings of them all. So it is that the sage (ruler), wishing to be above men, puts himself by his words below them, and, wishing to be before them, places his person behind them.
Rivers and seas receive the tribute of every valley stream because they are lower. Not because they are larger, not because they demand it — because water runs downhill and they are at the bottom. The chapter then makes the transfer explicit: the ruler who wishes to be above men puts himself below them in his words.
In this way though he has his place above them, men do not feel his weight, nor though he has his place before them, do they feel it an injury to them.
Men do not feel his weight. That is a precise thing to say about authority, and it is a test rather than a sentiment — if the people under a position can feel it pressing on them, the position is being held wrong.
Therefore all in the world delight to exalt him and do not weary of him. Because he does not strive, no one finds it possible to strive with him.
Because he does not strive, no one finds it possible to strive with him. The sentence closes the loop with chapter 8, where not wrangling about the low position meant no one found fault. Water does not win contests. It removes the conditions under which a contest could start.
Chapter 61: the same shape, at the size of a state
The image survives one more enlargement, and chapter 61 is titled, in Legge, The Attribute of Humility.
What makes a great state is its being (like) a low-lying, down-flowing (stream);--it becomes the centre to which tend (all the small states) under heaven.
A great state is like a low-lying, down-flowing stream, and becomes the centre to which the small states tend. The geography does the persuading. Nothing is conquered, and nothing needs to be, because the position was chosen so that arriving there is the natural direction of travel.
Chapter 61 then makes an argument by analogy that modern readers often find jarring, and it is worth quoting rather than paraphrasing.
(To illustrate from) the case of all females:--the female always overcomes the male by her stillness. Stillness may be considered (a sort of) abasement.
Stillness may be considered a sort of abasement. That is the whole water doctrine in six words — the low position and the still position are the same position, and both are described as what prevails rather than what yields.
The four read together
So the figure is one substance used four ways: water as conduct in chapter 8, water as force in 78, formlessness as access in 43, and the low place as a theory of authority in 66 and 61. Quoted alone, any of them reads like a proverb about being adaptable — the kind of line that ends up on a poster.
Read together they describe how influence actually moves: downhill, unopposed, early, and without a name on it. Harder to put on a poster, and more useful to have read.
Chapters 8, 43 and 78 are on this site in full, in James Legge's 1891 translation.