What does the word "begotten" mean?

Paul Thompson explains in this video that Isaiah describes Christ as a branch of the Lord. The word "begotten" generally means that it is not different or independent. It is actually the same thing. Christ is God in all of His existence. 

John 3:16 (NKJV) - "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life."

You know, Isaiah describes Jesus as the branch of the Lord. So to pick up that imagery of an arbor, an arborist, one who studies or looks at trees and sees that there are different ways that trees would reproduce. Like a pine tree, for example, drops its pine cones and another tree will come from it. That's a reproduction. That's a product that comes from.

Begotten is altogether different than this. It'd be more like, and obviously illustrations have limits and if we go too far in it we'll move into heresy, but more perhaps more in the understanding of like an aspen tree where a reproduction or a existence of an aspen tree shows up from the roots and it is actually a part of the tree. It's not a different tree. It's not an independent tree. It is of this.

And so begotten carries with it this significance that it's not something that is a product of the One, it is actually even the One. It's like light produces light, It doesn't produce a different kind of light. God produces God. He doesn't produce another God or a different God. He is God in all of His existence.

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