What does John 15:9 mean?

In prior verses, Jesus used the analogy of a vine and branches to explain the difference between those who merely "appear" to be Christians, versus those who are truly connected to the True Vine (John 15:1). Those "branches" which don't bear fruit are destined to be cut off and destroyed. Their permanent barrenness proves they were never attached to the lifegiving aspects of the vine in the first place (John 15:2–6; Matthew 7:21–23). Part of that analogy is Jesus referring to those who "abide in [Him]," and in whom His Word "abides."

Both of those facets are necessary to understand the statement given in this verse. Jesus' ministry has always been according to the will of God; what Jesus does, He does in submission to the Father (John 5:19). True "life" requires a natural connection, but abundance requires cultivation. Jesus passes down the love of God the Father to us, and we ought to continue to transmit that love, much as a branch transfers the life given to it from the vine. The means by which we do that is the same as it is for Christ: obedience.

When Jesus says to "abide in my love," He doesn't only mean to rest securely in knowing He loves us (Hebrews 4:15–16). He also means we are to actively live in the love He gives to us. That requires us to obey His teachings (John 14:15; 15:10).