Epidechomai combines epi (upon/in addition) + dechomai (to receive, welcome). It means to receive or accept someone — to welcome them in. It appears only twice in the NT, both in 3 John, in the contrasting portraits of Gaius (who receives) and Diotrephes (who refuses to receive).
The contrast in 3 John between welcoming and refusing to receive maps onto the fundamental choice of the gospel. Diotrephes "does not receive [epidechetai] us" and refuses to welcome the brothers. Gaius receives and shows hospitality to strangers. Jesus's words haunt the passage: "Whoever receives you receives me" (Matthew 10:40). The theology of reception runs through all of Scripture: Abraham receiving the angels, the disciples receiving the Spirit, the church receiving one another. To refuse the messenger of God is to refuse God Himself.