What does John 15:13 mean?

This statement is often used in reference to those who die—or are willing to die—in the service of other people. That's a valid interpretation, especially as Jesus is preparing the disciples for His impending arrest and death. However, there are additional applications to this teaching. The context of Jesus' statements about Christian life shows it's not "just" one's physical body which is in mind here. Christ has spoken about the need for Christians to "abide" in Him (John 15:4), which includes emulating His love (John 15:12).

In the prior verse, Jesus gave a command which is repeated several times in this conversation: to love each other (John 13:34; 15:12, 17). In this same discourse, Jesus identified obedience to His commands as a sign of true belief (John 14:15). He noted that Christians have no right to avoid those things Christ was willing to do for others (John 13:15–17). The ultimate act of love, of course, is to willingly offer one's life. For Christ to make such an offer to sinful people is indescribably merciful (John 10:17–18; Romans 5:7–8).

In daily Christian life, however, this verse still applies. Jesus' comments about following His commands, loving others, being humble, and so forth mean that "laying down one's life" is an attitude, as well as an action. When Jesus washed the feet of the disciples, He did something profoundly humble (John 13:3–5). Christian love is not meant to be "saved up" and exhibited only in grand gestures. Truly loving others, by "laying down" one's life, means "abiding" in the love of Christ (John 15:8–11), in a consistent, moment-by-moment approach.

The use of the term "friends" is important, as Jesus will clarify that He sees the disciples—and by extension, all believers—as His friends (John 15:14).