。
She looks very happy.
Literal
She [topic-は] very happy [seems-そう] [as-に] appears.
嬉しそうに見える stacks two evidentials — 嬉しそう ('looks happy' from impression) plus に見える ('appears as') — slightly redundant but emphasizing how visibly happy she is. The combination feels more vivid than either alone: 'gives every sign of being happy' rather than just 'looks happy.'