。
She kept me waiting for a long time.
Literal
She [topic-は] me [object-を] long-time caused-to-wait.
待たせた is the causative past of 待つ ('to wait') — 'caused to wait, made to wait.' The causative ~せる/~させる on a transitive-ish verb like 待つ standardly takes the person caused to act with を ('made me wait'); contrast に, which would feel more permissive ('let me wait'). 長い間 is a fixed adverbial phrase — 長い ('long') + 間 ('interval, span') — used for spans of time longer than 'a while.' The combination paints a familiar minor grievance: being kept waiting longer than feels reasonable.