。
She ignored the fact that he was sick.
Literal
She [topic-は] [he [subject-が] sick [is-である] [that-という]] fact [object-を] ignored.
~である is the formal/written copula, the literary equivalent of だ. ~という follows clauses and links them to a head noun like 事実 ('fact'), 噂 ('rumor'), or 報告 ('report') — a standard way to express 'the fact that ~' in formal writing.