We get the concept of "eternal life" from the Gospel of John.
And what St. John the Evangelist means by "eternal" isn't so much "a never-ending span of time," but rather, "a profundity of depth, breadth, and quality of life." Eternal life is first and foremost a life!--a life exemplified for us by Christ, his Blessed Mother, and the saints of old and up to the present day.
It's a life which is at the heart of our God, the Holy Trinity--a life of complete and utter self-gift to another. A life of absolute charity, total selflessness, complete joy and peace, and ecstatic union with our Beloved. The Church Fathers called it "perichoresis," or "the dancing around each other" of the Father, Son, and Holy Spirit. Eternal life is a share in this divine quality of life, characterized by the thrill of untainted love and fellowship.
And, since eternal life is about a "quality" of life, it's a life we should begin to live and experience . . . today! This is, ultimately, what our faith is geared toward, what our attempts at loving God and loving our neighbor are geared toward, and what all our deepest human desires are geared toward--"a profundity of depth, breadth, and quality of life," saturated by the purest outpouring of love, forever and ever.
We begin to experience eternal life is things such as: an embrace between true friends, deep feelings of gratitude and tenderness, being able to forgive and move on, and so on. The goal of our Catholic faith is to enter eternal life now (by loving God above all else, and loving our neighbors as ourselves; and enjoying the grace and mercy of our God), so that someday when we pass from this life, we will really die, but go on living (eternally) the eternal life--the quality of life--we began to live here.
Eternal life--it's today; it's forever.