。
She told me the story in secret.
Literal
She [topic-は] [secretly-内緒で] me [to-に] that story [object-を] did.
内緒で ('in secret, secretly') uses で in its manner sense — '(do something) in secret.' 内緒 ('secret, confidence') is paired with で adverbially or appears as 内緒の ('secret') as an adjective. ~に話をする ('tell ~ a story') uses 話をする as a light-verb construction.