Because this question is very general, I will focus on two poems in which I think Dickinson focuses expressly on individuality and on the importance of privacy.
Based on what we know for certain about Dickinson's life, she never married, only traveled once out of her native Amherst, Massachusetts to Boston, and remained rather secluded in the home in which she grew up in Amherst.
In her poem which begins "The soul selects her own society," one is tempted to think that Dickinson may be talking about herself. In this first line of the poem, Dickinson feminizes the Soul and undermines conventions of the time, which expected women to be socially outgoing and pleasing, by asserting that the soul "selects her own society/Then - shuts the Door." There is a sense of finality and assertiveness in this second line.
The public, characterized by "the Chariots," pause "at her low Gate" and "an Emperor be kneeling/Upon her Mat." Throughout these encounters, the Soul is "Unmoved."
The last stanza acknowledges that the Soul offers itself sufficient company:
"I've known her - from an ample nation/Choose One/Then - close the Valves of her attention/Like Stone-"
The Soul, or the individual, ultimately chooses herself. "The Valves" are an anatomical reference to the heart. She closes her heart off to others. "Like Stone" has a possible double meaning. A stone signifies coldness and steadfastness. However, it could also be the slab that encloses a tomb. Dickinson's expression of the narrator's choice to choose herself is ambiguous. Her refusals of "the Chariots" and the "Emperor" signify individualistic power, but loneliness seems to be equated with a kind of death.
In another poem, which begins, "I am Nobody! Who are you?" Dickinson contemplates fame. It is important to note that her poems were never published during her lifetime. Her narrator's view of fame is one of disgust:
"How dreary - to be - Somebody!/How public - like a Frog/To tell one's name - the livelong June/To an admiring Bog!"
She equates fame with being a frog. It is an ugly, odd-looking thing. The public is "an admiring Bog." A bog is a swamp that collects dead things, yet generates nothing. There appears to be a loss of individuality, a distortion of self, in becoming famous.
One can then conclude that individuality is a theme of tantamount importance in Dickinson's poems. Her expression of it is presented through the use of numerous literary devices (e.g., analogies, metaphors), and the subject may relate to aspects of her own personal life.