Jesus promises comfort to all sinners and people with heavy burdens who repent and come to Him. He takes away the burden of their sin. His peace is spiritual, it is inner serenity. His peace is freedom from fear and anxiety. His peace will last forever.
Worldly people seek peace and tranquility in religious rites and ceremonies and good deeds, but they do not find it. To find true peace and well-being, we must come to the true comforter, Jesus. True peace and tranquility cannot be found anywhere except in Jesus Christ.
The comfort that Jesus gives is not cessation of activity. Rather his peace is full of joy and praise, love and intimacy. It is full of the presence of God himself.