Jesus is saying that persecution should actually cause us to rejoice. There are many positive things about persecution but one of the best reasons to rejoice is because of the reward awaiting us in heaven.

Jesus takes the persecution of His saints very seriously as can be seen during the Damascus road experience of the apostle Paul. The Lord asked Paul (then Saul), "Why are you persecuting me?" (Acts 9:4) He didn't say, "Why are you persecuting my people?" but "Why are you persecuting me?"

It is not actually us that people are rejecting but they are rejecting the One we represent. Therefore, Jesus promised to share His reward with us. All the glory and honor that Jesus has and will receive will be shared with those who have suffered shame for His name's sake (Rom. 8:17). What a great reward!

Focusing on the reward instead of the persecution can actually make us rejoice when people speak against us (Acts 5:41). Paul actually longed to experience the fellowship that Jesus provided to those who suffered for His sake (Phil. 3:10). God's reward is infinitely greater than any suffering we will ever encounter.