There are several theories floating around regarding Dickinson's use of the dash, so no one is entirely sure what she specifically meant by it. Some people think that the transition from dependence on the exlamation point to dependence on the dash hints at her reasons. The poems with exclamation points were meant to be outcries, while in the dashed poems, the meaning lay more in the relationship between words so the dashes were meant to tie together unrelated words or images that might otherwise have remained unconnected. While the arrival to this conclusion differs depending on who you ask, this theory that the dashes were meant as bridges is a popular one.
Another possibility is that Dickinson wished for the poems to have a particular rhythm when read aloud, and the dashes are there to guide the reader through the right pauses.
Finally, her use of dashes may simply have been a result of her studies for Mount Holyoke Female Seminary. Dashes and capitalizing words within a sentence were appropriate grammatical choices according to William Harvey Wells' Grammar of the English Language, which is the grammar text upon which the seminary relied. Dickinson would have read this text when she was studying for her entrance into the school, and both the dashes and internal capitalization appear throughout her poems.