N Genesis 29 we have the record of Laban inviting Jacob to abide with him. The invitation was a 7-year invitation that turned into more than twice that length of time. In that context, it is easy to see what Laban meant. "Stay here. Continue with me. Remain in my house. Be a part of my family." As opposed to moving on to another place and looking for another opportunity, Laban offered to allow Jacob to dwell with him; to live with him.
That simple illustration is helpful in clarifying the doctrinal meaning of Christ's words in John 15. Jesus challenged His disciples to abide in Him. "Stay with Me! If you stand with Me and I stand with you, you will be spiritually fruitful." Jesus was not speaking about salvation, but of sanctification and service. He speaks of "branches" (John 15:2). A branch belongs to the vine & is an extension of the vine. If a branch is attached physically and continually to the trunk of the vine, it can be productive, but if the branch ceases to draw the sap from the vine, it cannot be fruitful. In fact, it will die. And what purpose is there in a dead or an unproductive branch? A farmer will surely cut away the dead wood from a vine in every case.
Jesus said, "I am the true vine, and My Father is the farmer" (John 15:1). We are branches "in Him" (John 15:2). We are His children; His offspring. As His children, we are pruned and improved continually. His words have a constant effect on us. He produces fruit through us – but only as we volitionally abide in Him.