When Jesus says, “Follow Me,” He means that we should mimic the pattern of His life – which is to humble ourselves in this life that we might be exalted in the life to come.
Jesus always avoided opportunities to be exalted in this earthly life. When the people wanted to make Him their king, He hid Himself. The time for His kingship would come later. This life was for service to others. And He tells us to imitate the way He lived.
As the apostle Paul wrote:
Do nothing from selfishness or empty conceit, but with humility of mind regard one another as more important than yourselves; do not merely look out for your own personal interests, but also for the interests of others. Have this attitude in yourselves which was also in Christ Jesus, who, although He existed in the form of God, did not regard equality with God a thing to be grasped, but emptied Himself, taking the form of a bond-servant, and being made in the likeness of men. Being found in appearance as a man, He humbled Himself by becoming obedient to the point of death, even death on a cross.
– Philippians 2:3-8
We truly follow the Son of God as we adopt this pattern of living.