。
She was busily devoting herself to her knitting.
Literal
She [topic-は] industriously knitting [at-に] effort [object-を] was-putting-out.
せっせと is a 擬態語 (state mimetic) for steady, focused, industrious activity — bees building, students cramming, anyone working away at something with concentration and energy. ~に精を出す is a fixed expression literally 'put out one's vital energy at X', meaning 'to throw oneself into / work hard at'. 精 here is the kanji of 精神 ('spirit') or 精力 ('vitality'), and the whole idiom carries an old-fashioned, slightly admiring tone — you might use it about someone diligently practicing a craft or pursuing a hobby. 編み物 ('knitting / knitted goods') is one of the prototypical handicrafts.