When she saw her mother, the girl burst into tears.

Literal

Mother [object-を] see-[conditional-と], girl [topic-は] bwah [quotative-と] started-crying

~を見ると = 'when (she) saw' — the conditional と for immediate/inevitable consequence. わっと = an onomatopoeia for bursting out (crying, shouting). 泣き出した = compound verb: 泣く (cry) + 出す (start) = to burst into tears.