As she grew up, she became more and more beautiful.

Literal

She [topic-は] grows [as-につれて], increasingly beautiful became.

ますます means 'more and more, increasingly' — an intensifying adverb that marks escalation over time. Combined with につれて, it creates a vivid image of beauty compounding as she matured. Contrast with 次第に (しだいに, 'gradually'), which is neutral and measured — ますます is more emphatic and dramatic, suggesting accelerating change.