to wait for something eagerly: to keep looking for what has been promised and is certain to come, but is not here yet
This is a waiting word, but not a restful one. It describes someone whose attention is fixed on something promised and still out of sight, and who keeps looking for it. The plainer Greek verb for expecting something (προσδοκάω) can be used of dreading a knock at the door as easily as of hoping for one, and the simpler verb it is built on (ἐκδέχομαι) covers ordinary waiting, such as guests waiting for each other at a meal. This word almost always leans toward what is longed for.
In the New Testament nearly every use points the same direction: forward, to the day Christ appears and the rescue he began is finished. Believers await a Savior from heaven, await the unveiling of the Lord, await the freeing of their bodies from decay. Paul sets the word beside a noun that pictures craning the neck to see something coming (ἀποκαραδοκία) and beside the word for holding out under pressure (ὑπομονή), and those two companions name the two halves of what it means: longing, and staying power.
One appearance turns the word toward God instead. In the days of Noah, while the ark was being built, God's patience waited. The straining forward drops away, and what is left is the same core act of holding a stretch of time open for something still to come.