Tsamach means to sprout, spring up, grow, or cause to grow. As a verb it appears about 33 times in the OT; the noun tsemach (branch, sprout) appears about 12 times. Both describe the emergence of new life from the ground — seed becoming plant, tree putting out a branch.
In agricultural Israel, tsamach evoked the wonder of life appearing from apparently dead ground — the miracle of germination and growth. This natural phenomenon becomes the primary prophetic image for the coming Messiah.
The Messianic Tsemach (Branch) is one of the most developed typological concepts in the Hebrew prophets. Zechariah 3:8 and 6:12 name the coming one explicitly: "I am going to bring my servant, the Branch (tsemach)" and "Here is the man whose name is the Branch (tsemach), and he will branch out from his place and build the temple of the LORD."
Jeremiah 23:5 and 33:15 promise: "I will raise up for David a righteous Branch (tsemach), and he will reign as king and act wisely." Isaiah 4:2 announces "the Branch (tsemach) of the LORD" as beautiful and glorious in the coming day of salvation.
The imagery is profound: from a stump that seems dead (Isaiah 11:1 — a shoot from the stump of Jesse), new royal life springs forth. The Davidic dynasty may appear cut down, but tsamach — the divine power of resurrection-life — erupts from the root. Jesus Christ is the ultimate Tsemach YHWH — the Branch of the LORD.