。
She watched the apple trees burst into bloom all at once.
Literal
[topic-は] apple [genitive-の] tree [subject-が] all-at-once start-blooming [nominalizer-の-を] saw.
~出す attached to the verb stem 咲き ('bloom') gives 咲き出す ('start to bloom, burst into bloom'). Compared to ~始める (the more neutral 'start to'), ~出す often carries a sudden, energetic flavor — fitting for a whole orchard erupting into blossom together. いっせいに ('all at once, in unison') reinforces the burst. The noun-modifying clause 咲き出す is nominalized by の and marked with を as the object of 見ました — this is the standard 'see X happen' pattern in Japanese, where the action being witnessed is wrapped in の and presented as a perceived event.