to groan or sigh: to let out the deep, wordless sound a person makes when pressed by pain, grief, or longing.
This is the breath you let out when words will not do: the heavy sigh of someone under a weight. It is not weeping with tears (κλαίω) and it is not a spoken complaint. It is the sound itself, the kind of groan you make almost without meaning to.
In the Old Testament Greek this plain human sound took on a deeper charge. When Israel groaned under slavery in Egypt, God heard the groan, remembered his promise, and came down to rescue them. From then on the word carried that whole story with it: a groan is the cry of the oppressed that God hears and answers. That background is why the New Testament writers reach for it.
When Jesus heals a deaf man he first looks up to heaven and groans, a sigh of compassion and prayer over a broken world. Paul turns the word toward the future: believers groan inwardly, not in despair but in longing, like people who know rescue is coming and cannot wait for it. He pictures the whole creation groaning the same way, straining toward the day it will be set free. The writer to the Hebrews uses it for a different ache, the heavy-hearted sighing of leaders worn down by a stubborn flock.
So the same sound runs across a wide range, from a sigh of pity, to the deep yearning of hope, to plain weariness of heart. What holds it together is that it is always the involuntary groan of someone under pressure, and in the Bible that groan is never the last word.