Jesus said to them, "I am the bread of life; whoever comes to me will never hunger, and whoever believes in me will never thirst. But I told you that although you have seen (me), you do not believe. Everything that the Father gives me will come to me, and I will not reject anyone who comes to me, because I came down from heaven not to do my own will but the will of the one who sent me. And this is the will of the one who sent me, that I should not lose anything of what he gave me, but that I should raise it (on) the last day. For this is the will of my Father, that everyone who sees the Son and believes in him may have eternal life, and I shall raise him (on) the last day." (Jn 6:35-40)
Jesus’ mission is to gather the people of God. He has not come to reject anyone who comes to him. He has come in the name of God and he will do the will of the Father. God has given him the mission and he has come to fulfil this mission by gathering all the people who belong to God.
One of the main requisite is to believe in Jesus. But the people are like the Israelites at the time of Moses. The Israelites grumbled against God and Moses. Similarly the people at the time of Jesus did not believe in Jesus and questioned him.
The promise that Jesus gives to the believer is the eternal life. It is not a life after death. It is the quality of life. It is sharing the inner life of Jesus. Eternal life is a sort of life that goes on even after death. This life begins already here and now for those who believe in Jesus. So eternal life is a new form of life for those who believe in Jesus and it begins here and now to be continued after death as a resurrected life.