She made her business a success.

Literal

She [topic-は] business [object-を] succeeded-made.

成功させた uses the causative form of the intransitive verb 成功する — she didn't succeed herself, she caused the business to succeed. This is a common use of the causative where the agent brings about an outcome rather than forcing a person to do something. Compare 成功した (it succeeded, intransitive) with 成功させた (she made it succeed, effectively transitivized via causative).