A couple things.....
1) We all labor for some form of food
No, this passage is not primarily talking about physical food, but rather what we fill our souls with. Every person on the planet tries to fill their lives with something. We all look to something to find our purpose, significance, security and life. We all look to find satisfaction in something. Here, Jesus confronts his audience by putting a fork in the road.
In one direction, is the life in pursuit of perishable food. This could be a number of things. Especially prevalent in American culture are financial security, academic prestige, vocational success, physical appearance, a care-free life, and happiness. For many of us, we look to these things daily. We eat of them daily with the hope that they will give us life; with the hopes that they will give us purpose, meaning, significance and security. The perishable food we pursue often time takes the form of obvious sin, but it is important to realize that not all perishable food has a marred appearance. In fact, many of the perishable things we pursue can be good things. Many of us look to relationships, to family, to love in order to fill us. These things certainly make a good appearance. However, they are in fact perishable. They do not give life. They do not satisfy. They only end in death. Imagine the crowd following Jesus in this story. They continued to follow Jesus because he miracously provided them with physical bread. Yet, they completely failed to realize the purpose of this miracle. It was to point them to Jesus the Savior, the only one who could give them real life. The crowd was completely ignorant to this and foolishly followed Jesus hoping to get more physical food. That is why Jesus asks them why they are seeking perishable food when imperishable food is offered to them. We are the same way. We ignorantly pursue perishable food, hoping it will satisfy us, hoping it will give us life. But we fail to realize that the Bread of Life has himself been given to us, to fill us, and to give us life as it was intended.
2) Jesus as the Bread of Life
Later in John 6, Jesus refers to himself as the Bread of Life. He himself is the imperishable food. Someone who eats or fills themselves with imperishable food eats of it, and it is never enough. They come back again and again. It doesn't stick. It doesn't fill the void. In Jesus' interaction with the following crowd, he offers himself as the source of this imperishable food. Jesus freely offers himself to those who seek him. Why then would we eat of anything else?
3) Jesus is only one qualified
How is it that Jesus is the one who can satisfy the hearts of men? Well, he answers this very question. Because the Father has set His seal on Him. Since Adam, mans heart has been restless. We have been trying to fix this, but something just isn't quite right. No matter how much success, comfort, prestige, happiness we have, we still are empty. Like Adam and Eve in the garden, we try to cover our shame. Deep down, we all know that there is lack of true life in us. That is because we are out of the fellowship for which we were created. Jesus is the only one qualified to restore this all-satisfying fellowship. All our desires and wants in this life only point to the one true desire for which we were created, and which will truly bring us satisfaction. Jesus gives true joy, true hope, true peace, true life. He is qualified to give this because from eternities past, the Father has set His seal on Jesus to be the Savior of the world. He is the one who is to restore the earth. He is the one whom the Scriptures speak of. THe Old Testament tells of His coming. By Christ's life, death and resurrection, a return to an all-satisfying fellowship is possible. This is what we were made for. We were made to eat of this food. Why tarry?
4) How do we eat this bread?
Jesus tells us what it means to do the work of God. Actually, the answer is sort of contradictory. Doing the work of God is actually believing in the One whom he has sent (Jesus). It is our human tendency to think what we can actively be doing to be right with God. However, Jesus tells us to do the work of God, is to believe in Him. It is a resting in Jesus. We eat of this bread by trusting in Christ and the work he has done. There is no work we can do to earn this imperishable bread. Therefore, to labor for imperishable food is to believe and trust in Jesus. Doing the work of God means to lean more heavily upon the Break of Life.