So, what is the significance of Jesus Christ being the Only-begotten Son of God?
1. Eternality as God.
David's use of this term "begotten" is expounded upon in Hebrews 1:5-8, which states concerning Christ's eternality: For to which of the angels did He ever say: “You are My Son, Today I have begotten You”? And again: “I will be to Him a Father, And He shall be to Me a Son”? 6 But when He again brings the firstborn into the world, He says: “Let all the angels of God worship Him.” 7 And of the angels He says: “Who makes His angels spirits And His ministers a flame of fire.” 8 But to the Son He says: “Your throne, O God, is forever and ever; A scepter of righteousness is the scepter of Your kingdom" (see also John 1:1).
The eternality of the Son is a fundamental truth in our understanding of Jesus Christ. Undoubtedly to say that He is the "only-begotten" Son means that He is eternal, but notice secondly...
2. Equality with the Father.
Theologians sometime refer to the Son's relationship to the Father as "filiation" and the Spirit's relationship to the Father as "spiration", carefully noting how these two distinct relationships express the One Divine nature or essence shared by all three-persons. The Nicene Creed for example, recited by Christians the world-over, has the following to say concerning the Father and the Son:
As one studies further into the theological language used to describe Jesus the Son, the term "begotten" would come to distinguish Him in His co-equality yet distinction from the Father concerning His Deity, whilst the term "birth" would describe Jesus in terms of His humanity derived from the virgin Mary.
To "beget" someone refers to the begetter and begotten sharing the same properties and being in the same class, without particular focus so much on the beginning of the life of the one begotten. When we consider birth on the other hand, the beginning of one's life is front-loaded into the very definition of what it means to be "birthed". Hence, Jesus was "begotten" touching His Deity - which is to say - He is uncreated, just like the Father.
3. Experiencing true humanity for your sake.