In this case, it's simply a quote from a counselor Manning spoke with, describing the moment when Manning first identified herself as female. [1]

This situation is typically referred to as gender dysphoria - the mismatch of sex assigned at birth with gender identity. For some trans people (Manning included) the most effective ways to resolve gender dysphoria may include hormone replacement therapy or surgery. There are lots of good articles on this if you want to read more about it, including a very good piece by a clinical psychiatrist for the NYT. [2]

[1] http://nymag.com/news/features/bradley-manning-2011-7/index4...

[2] https://www.nytimes.com/2015/08/23/opinion/sunday/richard-a-...