Euphraino means to rejoice, to make joyful, to celebrate with gladness. It can be used for joyful feasting, celebration, and communal merriment. The word is used both for earthly celebration (the parable of the prodigal son's feast) and for eschatological joy (Revelation 12:12). It derives from eu (well) + phren (mind/heart) — the state of being in good heart.
Luke 15 features euphraino at the climactic moments of all three parables of the lost: the father commands 'let us celebrate [euphraino]' when his prodigal son returns. The older brother refuses to join the celebration — and the parable ends with him outside the party. The theology is stark: to refuse to rejoice over the sinner's return is to refuse the character of the Father. In Revelation, the heavens are called to celebrate when the dragon is cast down. Eschatologically, the whole creation will euphraino when God's kingdom is fully established.