。
She was overcome with emotion and cried.
Literal
She [topic-は] emotion-overwhelmed [so-て] cried.
感極まって is the te-form of 感極まる ('be overcome with feeling'), the canonical lead-in for tears of overwhelming emotion — the kind of phrase you'd hear at weddings, graduations, reunions, and homecomings. The te-form binds the cause (being overwhelmed) to the result (crying) in tight sequence: feeling welled up, and tears followed. Importantly, 感極まる carries no negative weight — these are typically tears of joy, gratitude, or release rather than sorrow. The verb 極まる ('reach the extreme') applied to 感 ('emotion') paints a feeling pushed to its breaking point and spilling over.