What does John 14:21 mean?

Earlier in this passage, Jesus noted that those who love Him would obey His teachings (John 14:15). He followed that statement with reassurance that the Holy Spirit would come to be in believers (John 14:17). Our ability to follow the will of God depends on the influence of His Spirit (1 Corinthians 2:14–16). Later, Jesus will reinforce this idea of the Spirit guiding and teaching believers (John 15:26; 16:7–11).

Here, a person's obedience to Christ's teaching is presented as evidence that they do, indeed, have faith in Him. Good works cannot produce salvation (Titus 3:5), but salvation will produce an attitude of obedience (Romans 1:5). Passages such as James 2:18 echo this same sentiment. John, himself, makes note of this idea many times in his letters (1 John 2:3–6; 2 John 1:6; 3 John 1:11). At no point does Scripture suggest that we must do good to earn or keep our salvation. Yet, it frequently indicates that salvation influences our lives—where there is no such influence, there is no faith.

This idea of being "manifest" to the world follows from Jesus' earlier comment about the world not seeing or accepting the Holy Spirit (John 14:17). Those who reject God won't see Him—those who reject Christ reject God (John 14:9). Those who truly love God are those who accept Him, in faith, and receive the Holy Spirit (John 14:15–17). In a very literal sense, the world will no longer see Jesus—the crucifixion represents the end of His physical appearance to non-believers (John 14:19). In a spiritual sense, only those who accept Christ will see and understand God (1 Corinthians 2:14).

The "manifestation," so far as it applies to Christians, has a spectrum. For example, those who exhibit greater or more mature love for God will more readily understand Him (John 14:28).