to wait for or expect something one is sure is coming: to look ahead to a person's arrival or an event's outcome
This is the everyday New Testament word for leaning forward toward something you are sure lies ahead. The mind is fixed on the future and watches for it, whether that future is a person about to arrive or an event about to happen.
Sometimes what is awaited is welcome and longed for: a crowd waiting for Jesus, people watching for the promised Messiah, believers looking for new heavens and a new earth. Sometimes it is a plain reckoning that something will occur, good or grim alike: a servant caught off guard on a day he did not expect it, or bystanders expecting a snake-bitten man to swell up and drop dead. The single thread through both is anticipation, the future already held in view.
In Luke, Acts, and 2 Peter the word often carries the church's forward look toward what God has promised. It sits close to προσδέχομαι, which adds the note of glad welcome, and to the more intense ἀπεκδέχομαι, which strains eagerly toward the end.