。
She stared at me intently.
Literal
She [topic-は] me [object-を] fixedly looked-at.
じっと is a state mimetic (擬態語) for being still, fixed, and intent. With 見る it becomes 'stare fixedly,' with する it becomes 'stay still / hold still' (じっとしている), with 我慢する it becomes 'endure quietly' (じっと我慢する). The mimetic conveys focused, motionless attention — a held gaze with intent behind it. Distinct from ちらっと (the brief flicker of a glance) and じろり (a sharp judgmental sidelong look) — Japanese has a rich vocabulary of mimetics for the texture of looking.