。
She watched the bird in the nest carefully.
Literal
She [topic-は] nest [genitive-の] inside [genitive-の] bird [object-を] paying-attention seeing-fixedly.
巣の中の鳥 stacks two の's: 巣 ('nest') + の + 中 ('inside') + の + 鳥 ('bird') = 'the bird inside the nest.' 注意して is the te-form of 注意する ('pay attention, be careful') used adverbially — 'carefully, paying close attention.' 見つめる ('stare at, gaze at intently') is more focused than 見る — a sustained, attentive look rather than a glance.