Conjunctions, coordinators

In your case 'for' is a conjunction.

According to Oxford English English Dictionary (https://en.oxforddictionaries.com/definition/for):

FOR

CONJUNCTION

literary 

Because; since.

‘he felt guilty, for he knew that he bore a share of responsibility for Fanny's death’

As about the term 'coordinator' it's a synonym of 'conjunction'.

See in Oxford Living Dictionary:

Coordinator

2 Grammar  A word used to connect clauses, sentences, or words of equal syntactic importance (e.g. and, or, for)

‘subordinate clauses can be connected with a coordinator’ (https://en.oxforddictionaries.com/definition/coordinator)

Yes, it's a conjunction, albeit literary or archaic. "For" means "because" in this case, and is giving a justification or evidence for a preceding statement (see this question and answer for more details on this usage of "for").

Your quote comes from the Bible, and in context it says:

God sent "the Son of Man [to] be lifted up [crucified], that whosoever believeth in him should not perish, but have eternal life. For God so loved the world, that he gave his only begotten Son...." (John 3:14-16)

The quote you are interested in ("for God so loved the world that he gave his only begotten Son...") provides a causal reason for the action in the preceding statement (that Jesus, "the Son of Man," would be "lifted up.") The word "because" would have worked equally well here.

By the way, that full quote is all one thought; try to overlook the archaic punctuation of the King James translation of several hundred years ago!

As described in the other answer to this question, this usage of "for" is still reasonably common in literature.