Dedicated to the Lord Jesus Christ Who loved us, gave Himself for us, and washed us from our sins in His own Blood; and to the Church, which is His body.

In order to understand what eternal life is, it is helpful to understand what it is not. It is not just living forever. 
Everyone lives forever in either heaven or hell. Eternal life is not living forever in the blessings of heaven as to being tormented in hell.
John 3:36 and 5:24 show that eternal life is a present  possession of the believer.
Jesus describes eternal life as knowing God the Father and Jesus Christ.
Eternal life is having a close, personal relationship with God the Father and Jesus the Son.
According to John 3:16, this relationship with God is what salvation is all about. Forgiveness of our sins is not the point of salvation: closeness to the Father is. 
Jesus did die to purchase forgiveness for our sins because unforgiven sins block us from getting close to God. Sin was an barrier that stood between us and God. It had to be dealt with and it was. Anyone who views salvation as only forgiveness of their sins and stops there, is missing out on eternal life.
Salvation is to be the way to come back into unity with God. 
But, it is often presented as the way to escape the problems of this life and the judgment of hell later.
Most non-believers are so occupied with their "hell on earth" that they don't really think or care about their eternal future. They are fed up with religion and are looking for something that will fill the emptiness inside.
Only closeness (eternal life) with our Father can do that.