What does Matthew 5:11 mean?

This is part of Jesus' explanation of the Beatitudes: a series of statements about those who are "blessed," as proven by certain attitudes or actions (Matthew 5:1–9). In the previous verse, Jesus mentioned those who endured persecution for the sake of righteousness (Matthew 5:10). Here, He adds details about what persecution might look like and what might cause it. For the first time, Jesus moves away from general statements, given to His largely Jewish audience, and focuses more narrowly on Himself, specifically, as the One they are following.

The central issue in true Christian "persecution" is, of course, Jesus Christ. Merely being harassed or treated unfairly isn't necessarily persecution—especially if it's in response to our own wrongdoing (1 Peter 4:15). What Jesus means is that one proof of being "blessed" is willingness to endure unfair treatment on account of faithfully following Him (1 Peter 4:12–14). Those in opposition to Jesus might insult His followers, abuse them, and falsely accuse them of doing terrible things.

At the time Jesus gives the Sermon on the Mount, this hasn't yet happened to those who follow Him. However, this blessing serves as an early warning that such abuse is coming (John 16:1–4). In the following verse, Jesus will continue to explain why those who suffer for being connected to Him are blessed.