Formal greeting on first meeting. Often doubled — 幸会幸会 — and paired with 久仰 (jiǔyǎng, 'I have long admired you'). In casual settings 很高兴认识你 (hěn gāoxìng rènshi nǐ) is more typical.
memory
Read literally: 幸 (fortunate) + 会 (to meet) — 'fortunate to meet'. The same 幸 appears in 幸运 (lucky) and 荣幸 (honored).