The first thing that comes to my mind is a family tree.

From a temple standpoint we really emphasize searching out our family history. That history of often best represented with some form of a family tree. 

The Bible and the Book of Mormon contain extensive family pedigrees.

The idea of representing a family as a tree probably comes from Isaiah, who taught, "And there shall come forth a rod out of the stem of Jesse, and a Branch shall grow out of his roots:"

I generally think of the rod of the stem of Jesse as a symbol of Jesus Christ.

Malachi picks up this theme with his prophecy, "the day that cometh shall burn them up, saith the Lord of hosts, that it shall leave them neither root nor branch."

The family trees that we draw often work differently, but from a symbol standpoint, the roots are our ancestors and the branches are our descendants.

Right in the beginning of Genesis, trees show up in the creation story and trees are very important in the story of the fall. 

"And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good." Then "God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat."

Then there are some exceptions: "And the Lord God commanded the man, saying, Of every tree of the garden thou mayest freely eat: But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die."

Then after the fall: "So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life."

Axis Mundi

A tree is planted in the earth. Its roots spread out and provide it a firm hold.

It extends upwards. Its branches reach up for the sky.

Each tree is a type of "world axis" where heaven meets earth. 

This is a commonly part of "tree of life" symbolism. 

This was an important symbol in Lehi's dream. The tree was a symbol of the love of God, or even more simply, a symbol of God. 

In the Noah story, it is an olive branch that the dove brings back. An olive branch remains a symbol of peace today.

Zenos shared an extended allegory about olive trees. They remind us of God's plan for scattering and gathering Israel. It is quoted by Jacob and also taught by Lehi and Paul.

When I was in Israel, I learned that olive trees can grow back from their roots. So, we know those trees in Gethsemane are more than 800 years old but we do not know how old their roots are. 

The Doctrine and Covenants gives us an alternate interpretation of the "root of Jesse." "Behold, thus saith the Lord, it is a descendant of Jesse, as well as of Joseph, unto whom rightly belongs the priesthood, and the keys of the kingdom, for an ensign, and for the gathering of my people in the last days." This descendant is clearly important in the restoration.

Isaiah connects the idea of regeneration with a teil or oak tree, "But yet in it shall be a tenth, and it shall return, and shall be eaten: as a teil tree, and as an oak, whose substance is in them, when they cast their leaves: so the holy seed shall be the substance thereof."

Jesus suffered in the Garden of Gethsemane. He felt the burden of all sins and suffering. Just like the olive that was pressed for oil, Jesus bleed from his pores under such a press. Trees, especially olive trees can help us remember this sacred, infinite event.