Before you can really understand what Matthew 5:10 means, you have to understand and be living the rest of the Beatitudes.
If you are living a life that is poor in spirit, that mourns over your sin, that lives meekly through His strength, that hungers and thirsts after righteousness, that is merciful, pure in heart, and making peace…then you will be exceedingly glad for the persecution that comes your way.
You see, the world is going in the opposite direction and they are trying to push you into their mold. Yet you are a twice-born man among once-born people, and you are going to go against the tide.
It costs to serve Jesus Christ—every day and every step. But you are blessed! When was the last time you took some flack for Jesus? Great is your reward in heaven.