Genesis 2:9 first notes the presence of the Tree of Life in the center of the garden of Eden:
The Lord God made all kinds of trees grow from the soil, every tree that was pleasing to look at and good for food. (Now the tree of life and the tree of the knowledge of good and evil were in the middle of the orchard.)
Genesis 2:16-17 states:
Then the Lord God commanded the man, “You may freely eat fruit from every tree of the orchard, but you must not eat from the tree of the knowledge of good and evil, for when you eat from it you will surely die.
Presumably, every tree in the garden included the Tree of Life, since Adam and Eve were only forbidden from consuming fruit from the Tree of the Knowledge of Good and Evil.
In Genesis 3:22-24, God states:
And the Lord God said, “Now that the man has become like one of us, knowing good and evil, he must not be allowed to stretch out his hand and take also from the tree of life and eat, and live forever.” So the Lord God expelled him from the orchard in Eden to cultivate the ground from which he had been taken. When he drove the man out, he placed on the eastern side of the orchard in Eden angelic sentries who used the flame of a whirling sword to guard the way to the tree of life.
What becomes clear then, is that by eating of the Tree of Life, Adam and Eve are like God - they have everlasting life. By forbidding Adam and Eve from eating the fruit of the Tree of Life, God is instituting the promised consequence ("You shall surely die") and if God continued to allow them to eat from the Tree, Adam and Eve would not die, but instead would live forever and have eternal Life.
According to Romans 6:23:
For the payoff of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.
Revelation 22:1-3 makes it clear that after the rapture, we will be able to partake of this tree again:
"Then the angel showed me the river of the water of life—water as clear as crystal—pouring out from the throne of God and of the Lamb, flowing down the middle of the city’s main street. On each side of the river is the tree of life producing twelve kinds of fruit, yielding its fruit every month of the year. Its leaves are for the healing of the nations. And there will no longer be any curse, and the throne of God and the Lamb will be in the city. His servants will worship him, and they will see his face, and his name will be on their foreheads."
From this passage we see that the Tree of Life produces 12 kinds of fruit (for the 12 tribes of Israel with which God made the Covenant*), that the Tree of Life's leaves are for the healing of the nations (of Israel), And there will no longer be any curse (The curse of Genesis - that by eating of the Fruit, Adam and Eve would not have eternal/everlasting life).
As Paul makes clear in his epistle to the Galatians, all believers are members of the nation of Israel to which the Covenant to give Abram's descendants the promised land was made. Galatians 3:29 states,
If you belong to Christ, then you are Abraham's seed, and heirs according to the promise.
And the promise of the promised land, was not just the promise of the land that is now Israel, but really a promise to give back the Garden of Eden and the Tree of Life contained therein vis-a-vis, the sacrifice of the Messiah (Jesus Christ). In God's promise to Abraham, you will note in Genesis 15:18 it says:
That day the Lord made a covenant with Abram: “To your descendants I give this land, from the river of Egypt to the great river, the Euphrates River
This is the same land in which the Garden of Eden is located according to Genesis 2:10:
Now a river flows from Eden to water the orchard, and from there it divides into four headstreams. The name of the first is Pishon; it runs through the entire land of Havilah, where there is gold. (The gold of that land is pure; pearls and lapis lazuli are also there). The name of the second river is Gihon; it runs through the entire land of Cush. The name of the third river is Tigris; it runs along the east side of Assyria. The fourth river is the Euphrates.
And just as Eden is described as a paradise, the Promised Land is said to be "Flowing with Milk and Honey" which is the probable origin for the belief that the Promised Land included the Garden of Eden.
According to Young Earth Creationism, the Tree of Life provides the everlasting or eternal life that was present in the Garden of Eden and was promised to us in Romans 6:23 ("the gift of God is eternal life") and at the end of time.