The account of what happened is fairly brief: "As Jesus walked beside the Sea of Galilee, he saw Simon and his brother Andrew casting a net into the lake, for they were fishermen. 'Come, follow me,' Jesus said, 'and I will make you fishers of men.' At once they left their nets and followed him" (Mark 1:16-18).
We do need to understand that this wasn't the first time Andrew and his brother had seen Jesus; they had spent a day with him once, listening to his teachings. (John 1:35-42). Still, I can't help but be amazed at what happens when Jesus called these men. They left their nets and followed him. More than nets, they left their father and a thriving fishing business. They left their home and the life they knew.
How did Jesus convince them? Did he lay out an educational plan of the training they would receive over the next few years? Did he discuss health coverage and benefits? No. Jesus didn't even talk to them about eternal life, the greatest benefit of all. He merely said, "Come, and I will make you fishers of men."
Jesus offered them a life of purpose. He offered them the chance to be involved in the work that God is doing in this world. That was enough to make them leave the comfortable life they had.
Jesus still says, "Come, follow me." There's more to it, of course, but in the end, it comes down to a simple invitation. Come. Come let me give purpose to your life. Come be a part of God's activity in this world.
If you are totally satisfied with your life now, if you have no desire to do more and be more, then Jesus' offer won't interest you. If you're pleased with the present state of the world and don't feel any urge to work to make it better, you may not see the point.