Pempo (πέμπω) means to send or dispatch — to cause someone to go, to commission and release. It is one of two primary Greek words for 'send' (alongside apostello), and the distinction between them is theologically significant in John's Gospel: pempo emphasizes the authority and act of the one sending, while apostello emphasizes the official commission and authority given to the one sent.
John's Gospel uses pempo predominantly for God the Father sending the Son: 'For God so loved the world that he gave his one and only Son' — John 3:16 uses didomi but the sending theology is pempo. Jesus repeatedly says 'the one who sent me' (ho pempsas me) — grounding His entire mission in the Father's authoritative dispatch. The Spirit is also pempo-ed by the Father (John 14:26). The whole gospel is a sending.
The 'sent' theology of John — using both pempo and apostello — establishes that Jesus is not a self-appointed teacher but the Father's dispatched representative. This is the foundation of apostolic authority: the apostle (apostolos) is one sent with the sender's authority. Jesus tells His disciples: 'As the Father has sent me, I am sending you' (John 20:21) — the pempo/apostello mission continues in the Church.