What is the meaning in the Bible for the "Branch"? In the Bible in Zechariah 3:8-10, 6:12-13, Isaiah 4:2-3 mention the Branch. What are they talking about?
Jesus is prophetically referred to as "the branch of David" (Is 11:1) and a "branch from the roots of Jesse" (Jer 33:15).

In general, "branch" can refer to offspring and "root" to parents (think "family tree"). Children can be referred to as "fruit" ("be fruitful", "fruit of the womb", "house of Judah ... bear fruit", "fruit of my body")