翘首以待 is a four-character idiom meaning 'to eagerly await something, often with great anticipation or anxiety'. The literal image is 'to crane one's neck and wait' — you physically stretch your neck to look for what's coming. It's a formal, literary expression used in news headlines, speeches, and written announcements. Unlike the more casual 等不及, this phrase carries a sense of dignified, hopeful expectation.