What is the LDS definition of "Divinity"

Perhaps the greatest difference between mainstream Christianity and LDS theology lies in this point:

The mainline definition of "divinity" includes "Within Christianity it belongs to God alone". Since the "mainstream" understanding of who Christ is is that Jesus is God, not a physical/spiritual son of God, this bears on the doctrine of the Trinity.

As Latter-Day Saints do not accept the doctrine of the Trinity, of course this understanding of divinity is meaningless within LDS theology.

The Nicene Creed teaches that the Son is "begotten, not made" and is "of one substance with the Father." This is a somewhat odd choice of words if its intent is to convey an understanding of the nature of God, as something that is begotten--the word refers to the act of having a child--has its own physically separate "substance" (body) from that of its parent(s).

By contrast, Mormonism strives for clarity in this area. One revelation teaches that:

The Father has a body of flesh and bones as tangible as man’s; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us.

- Doctrine and Covenants 130: 22

As the FAIR article linked to in the question notes, Jesus is held to be a spirit son of God, just as all mankind is. And this is important to understanding the LDS concept of divine nature. All living beings reproduce and multiply after their own kind. A giraffe has little giraffes, a cat produces more cats, a tree's seeds grow into the same type of tree, and so on. But the highest of living beings is mankind, who was explicitly made in God's image and likeness, and our spirits are directly his children. By the same principle, we carry his divine nature in an immature state, like any child that has yet to grow up.

The divine nature of Jesus is described in Doctrine and Covenants, section 93:

21 And now, verily I say unto you, I was in the beginning with the Father, and am the Firstborn;

22 And all those who are begotten through me are partakers of the glory of the same, and are the church of the Firstborn.

23 Ye were also in the beginning with the Father; that which is Spirit, even the Spirit of truth;

24 And truth is knowledge of things as they are, and as they were, and as they are to come;

25 And whatsoever is more or less than this is the spirit of that wicked one who was a liar from the beginning.

26 The Spirit of truth is of God. I am the Spirit of truth, and John bore record of me, saying: He received a fulness of truth, yea, even of all truth;

27 And no man receiveth a fulness unless he keepeth his commandments.

28 He that keepeth his commandments receiveth truth and light, until he is glorified in truth and knoweth all things.

29 Man was also in the beginning with God. Intelligence, or the light of truth, was not created or made, neither indeed can be.

We read here that:

• Jesus was with the Father in the beginning. Mankind was also, but the distinction is made that Christ was the Firstborn.
• Unlike the rest of mankind, Jesus "received a fulness of truth," which can only be received by obedience to the commandments of God.
• It is only by being "begotten through me"--what Elder M. Russel Ballard, quoted in the FAIR article, calls being "born again as His sons and daughters in the gospel covenant"--that mankind can partake of his glory.

Here we see the essential difference that makes Jesus more than simply "a son of God," but rather "the Son of God." He had received a fulness of truth from the beginning. He is truly divine in every sense of the word, and has been from the beginning. "By him, and through him, and of him, the worlds are and were created, and the inhabitants thereof are begotten sons and daughters unto God." (Doctrine and Covenants 76:24)

In summary, the question asks:

The LDS position is that Jesus is a separate being from God, but is still divine.

Clearly this means that the LDS Church must have a different understanding of the term "divinity". Divinity must not be applicable to "God alone" if Jesus is not God, and Jesus is divine.

To which the Latter-Day Saint would respond that Jesus is a separate being from the Father, but this should not be understood to mean that "Jesus is not God" in any sense, but rather that the Father and the Son (and the Holy Ghost) are separate, distinct beings, who are one in purpose, in knowledge and understanding and will, but not in substance, and work in harmony as God.

However, having clarified that, divinity is still not seen as being applicable to God alone, because it also applies to his children (us), in an immature or embryonic form. However, that is the subject for another question, as going into it in any depth could make this answer much longer than it already is and take it well off-topic. It's important to note, though, that Latter-Day Saints hold this to be the very highest part of God's plan:

For behold, this is my work and my glory—to bring to pass the immortality and eternal life of man. - Moses 1:39

Eternal Life is spoken of as here something distinct from immortality (being resurrected to a deathless and physically perfect state); it is defined elsewhere as a quality of life that is like the life of God, who is Eternal, and helping us to achieve this is God's "work and glory."