To "abide" means to accept or act in accordance with a rule, according to the Apple Dictionary Application. To "abide in Christ" would then by definition mean to accept Christ all that He is and to act in accordance to His rule and His teachings.
In John 15 Jesus gives the metaphor of Him being the "true vine" and what I would consider all created people to be the branches. Jesus equates God the Father to the Gardener who prunes the branches, which do not produce fruit. Those who do not produce fruit would be considered, in my mind, to be non-Christians. Christ-followers, those who abide in Christ, produce fruit because they are tied directly to their source of life, the True Vine. If a branch is not producing fruit it's not part of the True Vine. If one is connected to the True Vine the branch MUST produce fruit. It is a natural process of being connected to the true vine.
To "abide in Christ" one must first know Christ as Savior, then the process of gleaning from their relationship with Jesus must take place in order to grow and produce fruit. While all Christ-followers produce some sort of fruit, just as a fruit bearing plant that is watered daily and fertilized grows better fruit that one that is not, the same is true with the Christ-follower. The more time spent exercising spiritual disciples such as spending time in the Word of God and in prayer the higher quality of the fruit produced.
"Abiding in Christ" is a way of life. It's a complete acceptance of Christ as the ultimate ruler and His teachings as the ultimate rules for life, but not only to accept these things but also to live them out. Jesus himself says in John 15 that if one does not remain in Him that they can do nothing. So not only is it vital for the life of the Christ-follower to spend time “abiding in Christ”.