Emily is talking about the danger of having either too much or too little in the place in your life where you draw upon for strength and hope – in other words, your well spring, or perhaps your well-being spring. She doesn’t say what exactly this place is – it’s not actually a brook – but for each of us we have that secret place inside all of us that is like our garden.
What is interesting about this poem is how she describes this “Brook” as “little” and follows it up with the adjectives “bashful”, “blushing”, and “tremble”. She creates the image of this “Brook” as being delicate, easily frightened, and something that requires great care and tenderness to maintain. When we look in the OED, we learn that “Brook” as a verb can mean “to enjoy the use of, make use of, profit by; to use, enjoy, possess, hold” and she relates this to the “heart”, not just physically if we imagine the blood flowing through the brook-like channels of the heart’s circulation, but also in relation to our spirit. Yet this well being must be carefully tended.
In the second stanza she describes how this place is a secret place from the outside world because “nobody knows”, yet this is somewhat ironic because she is saying we all have this place, but it’s a secret from everyone too. She continues this puzzling aspect of something everyone has as also being something “nobody knows” with the word “still” which can mean that it is “still” there regardless of it being a secret, but also in the sense of it being “still” as in it not moving, or at least not moving fast enough for anyone to notice.
Another way to think of this idea of a secret that everybody knows “nobody knows” and of it being “still” yet moving is to think of a poem, such as “Water, is taught by thirst“, which is one of my favorites (but any poem you love will work). This poem is common knowledge since anyone can read it, but it is a secret to you because of how much it means to you when it might not mean the same (or anything at all) to someone else. The poem is also “still”, not just in the sense that it is a “still” object but that it is always there on the page and yet it moves you whenever you read it.
And if we push the idea that the thing she is talking about is a poem (or art more generally), then in the third stanza she builds upon the metaphor of a “Brook” being a place of joy for our heart by transforming the poem into a poem about the importance of maintaining our “little brook”. Emily has many times talked about how we should value even the smallest things that mean something to us, such as in “By Chivalries as tiny“, and here she explains why this is important because they are delicate and require great care. In this sense she is also talking about the act of creation, such as creating a work of art, and this poem describes the process as she builds it up one line at a time, as if each line were a little brook and secret world unto itself, and she also describes the dangers of letting it overflow with a torrent of spring floods or an overabundance of energy in the “burning noon” of life’s “August” which, incidentally, is not just the month, but also means “to ripen” and bring to “fruition” (OED).
So one reading of this poem can be that she is writing about writing, and we can imagine the “little brook” as the ink running from the pen to the paper, but if there is too much energy then the ink will run too fast and the poem will overflow and destroy the image of a timid brook by becoming a flooded mess on the page which is unreadable, yet if we neglect our art and let the ink dry, then nothing will flow from our pen and we will be unable to express what is in our heart.