While thinking through what it means to abide in Christ, here His words come through.
So Jesus was saying to those […] who had believed Him, “If you continue in My word, then you are truly disciples of Mine; and you will know the truth, and the truth will make you free.” – Jn 8:31
That is to say, to abide in Him is to abide in His word. That in doing so, the fruit of that is to live without pervasive sin. That is the bearing fruit He speaks of further along in His teaching.
“I am the vine, you are the branches; he who abides in Me and I in him, he bears much fruit, for apart from Me you can do nothing.” – Jn 15:5
That is we are unable to do anything good or of benefit to ourselves and the kingdom if we were to no longer abide. To dwell in Him is to be free from sin. Able to serve and honor Him with fruit by being of good use to the Lord and others.
Another really incredible point to carefully think through is that God Himself keeps us dwelling. We are responsible for whether or not we abide, but it is Jesus that causes our faith to remain (Jn 17:11-12). Once we are sealed by the Holy Spirit, it is He who causes us to turn back if we might doubt, neglect, or deny Christ. Moreover, in John Piper‘s words, it is Jesus’ demand that we abide in him so that we keep trusting the one who keeps us trusting.
We remain attached to Jesus by abiding in Him through His word.
1 John Piper, What Jesus Demands from the World (Wheaton, IL: Crossway Books, 2006), 67.