We're throwing a farewell party for Nancy tomorrow.

Literal

Tomorrow Nancy [possessive-の] farewell-party [object-を] open.

開く is the standard verb for 'holding / opening' events — 会議を開く (hold a meeting), パーティーを開く (throw a party). お別れ会 is a set compound: honorific お + 別れ ('parting') + 会 ('gathering').