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She generously shared the benefit of her insight with them.
Literal
She [topic-は] her own insight [called-という] benefit [object-を] them [to-に] give [casual benefactive-てやった].
~という here labels the noun 利益 ('benefit') with the descriptive content 洞察力 ('the power/faculty of insight'): 'the benefit (which is) her insight.' 与える ('to give, grant, bestow') is a formal/written verb of giving. ~てやる adds a casual or condescending benefactive nuance — 'she did them the favor of giving,' with a faint undercurrent of 'as if to underlings,' which can fit a literary or slightly ironic tone.