Receiving Christ is entrusting oneself to Jesus as He is revealed in the gospel — taking Him as Saviour and Lord rather than merely seeking His gifts.
John says that as many as received Him, to them He gave power to become the sons of God, even to them that believe on His name. Receiving and believing belong together. To receive Christ is not to add Him to a life one still governs, but to rely upon Him, yield to His rightful authority, and belong to Him.
It is the same decisive turning described as believing, repenting, surrendering, and calling on His name: the sinner entrusts himself to Christ, and through Him becomes a child of God.
See in Scripture: John 1:10–13; John 3:14–18; John 6:35–40; Colossians 2:6–7