This has always been a puzzlement for me. I thought that there is going to be one eternity so why do Mormons speak of eternities? What exactly is an eternity and what is the meaning of eternities? And what are the eternities going to consist of?
There are a few interesting issues at play in your question. First, there’s the language. From a certain perspective, there’s no difference in eternity and eternities. It’s just the way you say it. Like, “In the eternities…” would mean the same thing as “For all eternity…”.
From another perspective, we don’t really know, because eternity is a reference to time, and time doesn’t necessarily function the same way for an exalted being as it does for us. God sees all things, past, present and future before Him constantly. In Moses 1:6, for example, we read:
“but there is no God beside me, and all things are present with me, for I know them all.”
…and D&C 38:2:
“The same which knoweth all things, for all things are present before mine eyes;”,
…and D&C 130:7:
“But they reside in the presence of God, on a globe like a sea of glass and fire, where all things for their glory are manifest, past, present, and future, and are continually before the Lord.”
…and so forth. Perhaps that plays into the meaning of eternities a bit.
Finally, we have the idea of “eternal lives” as in D&C 132:24 “This is eternal lives—to know the only wise and true God, and Jesus Christ, whom he hath sent. I am he. Receive ye, therefore, my law.” This is another strange pluralization of a word that has been explained to us by Bruce R. McConkie:
“Those who gain eternal life (exaltation) also gain eternal lives, meaning that in the resurrection they have eternal ‘increase,’ ‘a continuation of the seeds,’ a ‘continuation of the lives.’ Their spirit progeny will ‘continue as innumerable as the stars; or, if ye were to count the sand upon the seashore ye could not number them.’ (D&C 131:1–4; 132:19–25, 30, 55.)”
Perhaps eternities is correlative to eternal lives and the continuation of our seed. We will have eternity. Our seed will also have eternity. Their seed will have eternity. Hence we get eternities instead of just one eternity.
For a much greater in depth read, see an article I wrote in 1993 There Shall Be Time No Longer.