IDIC: Infinite Diversity in Infinite Combinations

"Intolerance in the 23rd century?  Improbable!  If humankind survives that long, we will have learned to take a delight in the essential differences between people and between cultures.  We will learn that differences in ideas and attitudes are a delight, part of life’s exciting variety, not something to fear.  It’s a manifestation of the greatness that God, or whatever it is, gave us.  This infinite variation and delight, this is part of the optimism that we built into Star Trek."

Gene Roddenberry

"The glory of creation is in its infinite diversity—and the ways our differences combine to create meaning and beauty."

The triangle and the circle are two different shapes, materials, and textures. They represent any two
diverse things which come together to create truth or beauty, represented by the jewel in the center.

IDIC (from the Star Trek Concordance, 1976):

The most revered Vulcan symbol, combining variations in texture, shape, and color.  The name is Terran, an acronym for “Infinite Diversity in Infinite Combinations”; the Vulcan name is not known. (This has changed since 1976, see below)

Spock‘s IDIC, which can be worn as a pin or as a pendant, is a circle and triangle of white and yellow-gold metals in shiny and textured (or Florentine) finish, with a white jewel. Spock explains that the different shapes and materials represent the diverse things which come together to create truth and beauty; the glory of creation lies in its infinite diversity and meanings. (Is There in Truth No Beauty?”)

Kirk recalls to the Spock-clone the philosophy of the Vulcan IDIC and what it means.  He also asks if an army of Spocks could impose peace on the galaxy and make other beings accept the Phylosian philisophy in defiance of the Vulcan IDIC concept.  The Spock-clone decides that it cannot be done. (“The Infinite Vulcan”)

The above text is taken from The Star Trek Concordance by Bjo Trimble, 1976

From the vulcan-l
Vulcan FAQ:

Steve Boozer has this additional item:

According to the unnamed Vulcan Master who tutored teenaged Tuvok, it is called kol-ut-shan – “the cornerstone of our beliefs” [VOY “Gravity”].
In fandom the IDIC is also called t’triahve.
In Traditional Golic Vulcan the term used is Va’Vuhnaya s’Va’Terishlar. Another term for the concept is Kol-uchang.

"Is There in Truth, No Beauty?"

The IDIC medallion first appeared in the third season of the original series in the episode "Is There in Truth, No Beauty?" with an explanation of it’s symbolism given in the dinner scene. The complete version of that explanation was not in the aired version of the episode, but was in the final, unfilmed draft. Following are both versions—research and italicized comments by Greg Schnitzer.* 

Script as aired
The aired version–the Revised Final Draft of “Is There In Truth, No Beauty?” written by Jean Lisette Aroeste, dated July 17 1968 has the following dialog related to Mister Spock‘s IDIC (Infinite Diversity Through Infinite Combinations) medallion–first at the dinner for Dr. Miranda Jones and then at the end as she beams out:

Script as written
The Final Draft, dated July 16, 1968 actually is a bit longer and has more information about the IDIC.
(The scene is the same dinner scene with Doctor Jones.)

I was just noticing your Vulcan IDIC, Mister Spock. Is it a reminder that, as a Vulcan, you can mind-link with the Medusans far better than I could?
Well, I doubt that Mister Spock would don the most revered of all Vulcan symbols merely to annoy you, Dr. Jones.
As a matter of fact, I wear it this evening to honour you, Doctor.
Very interesting. I might even say fascinating, but back to your mission. (Later, in the Transporter Room....)
I understand, Mister Spock. The glory of creation is in its infinite diversity.
And the ways our differences combine to create meaning and beauty.

Busy with the search for expressing her thoughts, Miranda's hand touches the medallion pinned to Spock's breast.  She touches it carefully, as though identifying it.  McCoy sees the fleeting gesture her hand makes on contact with the medallion.  He is very intent on her action.

Spock pulls back, afraid he may have scratched her.

Forgive me. I forget that dress uniforms can injure.
No, I was merely looking at your Vulcan IDIC, Mister Spock.
(looks up, curiously)
Is it a reminder that as a Vulcan you could mind-meld with the Medeusan much more effectively than I could?
(to the others, but smiling)
It would be most difficult for a Vulcan to see a mere human take on this exciting a challenge.
(to Spock)
Interesting question. It is a fact that you rarely do wear the IDIC.
I doubt that Mister Spock would don the most revered of all Vulcan symbols merely to annoy a guest, Dr. Jones.
(to Miranda)
In fact, I wear it this evening to honor you, Doctor.
Indeed. Perhaps even with those years on Vulcan, you missed the true symbology.
(indicates medallion)
The triangle and the circle... ...different shapes, materials, textures...represent any two diverse things which come together to create here...truth or beauty.
(indicating the parts, looks up)
For example, Doctor Miranda Jones, who combined herself and the disciplines of my race, to become greater than the sum of both. Kirk can see Miranda isn't fully sold on Spock's intentions ...he changes the subject.
Very interesting, I might even say...fascinating.

“Mankind will reach maturity on the day it learns to value diversity—of life and ideas. To be different is not necessarily to be ugly; to have a different idea is not necessarily to be wrong. The worst thing that could happen is for all of us to look and think and act alike. For if we cannot learn to value the small variations among our own kind here on earth, then God help us when we get out into space and meet the variations that are almost certainly out there.”

Gene Roddenberry

More information about the IDIC is here.