Jesus repeated the word ABIDE several times in John 15. He said it often, because it was extremely important to Him that we hear His message loud and clear. His emphasis to His disciples then and now is that He lives within us, even though He is no longer physically among us. If we are His, then we have a constant connection with Him. He abides in us.
Another key part of this message is that a disciple of Christ must do his or her part to abide in Him. Jesus said it is essential to have this intimate connection- Him in us and us in Him- so that we can make a lasting impact on the world around us. He called this impact fruit, and He drew a picture for us: "I am the vine; you are the branches. Whoever abides in Me and I in him, he it is that bears much fruit, for apart from Me you can do nothing." John 15:5 ESV