。
She's putting all her energy into her work.
Literal
She [topic-は] work [target-に] vigor [object-を] is-putting-out.
精を出す ('to put out one's spirit/vigor') is a fixed collocation meaning 'to work hard, throw oneself into, give one's all.' 精 ('spirit, energy, essence') is an evocative noun appearing in many compounds (精神 'mind/spirit,' 精力 'vitality,' 精進 'devotion'). The に marks what one is throwing oneself into. The progressive ~ている marks an ongoing exertion. A slightly old-fashioned but warm phrase, often used to commend dedicated effort.