Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A hypothetical massless, neutral elementary particle believed to mediate the strong interaction that binds quarks together.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A massless gauge boson that binds quarks together to form baryons, mesons and other hadrons and is associated with the strong nuclear force.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a gauge boson that mediates strong interaction among quarks
Etymologies
Examples

One of the bosons there are four flavours sticks them together and is called a gluon, which sounds like glue and is therefore probably the easiest concept out of all of this comprehend.

I think the interiors of black holes are dual to a condensate phase of gauge fields, such as gluon plasmas probed at RHIC, and that these objects are determined by a dilaton field to contain information for an AdS (AntideSitter) spacetime and its conformal infinity.

How the proton gets its spin out of the quarkgluon shimmy is still a big mystery, so theorists have been experimenting with difference ways to combine PDFs and form factors, to include interference terms, and understand all components of nulceon spin.
Generalized PDFs Imply a Gravitomagnetic Moment!?!?!? « Imaginary Potential

If you are operating at first order, the vanilla type of PDFs naively tell you what the probability of finding a quark or gluon of a certain type and certain longitudinal momentum is.
Generalized PDFs Imply a Gravitomagnetic Moment!?!?!? « Imaginary Potential

The goal is to study lots of processes, but most significantly to create really hot, dense conditions where we may be able to observe a phase transition in QCD to something called the quarkgluon plasma.

Anonymous (the previous) isn't all wrong: photons do mediate the electromagnetic force which is key for holding molecules together (and therefore the size of particles as addressed in this post)... sadly, for anonymous you kind of also need the weak (bosons) and strong (gluon) forces to hold nuclei and atoms together, respectively.

Achieved at the almost speed of light collision of gold ions, this resulted in the temporary existence of quarkgluon soup – something first seen at about ten to the power of minus twelve of the first second after the big bang.
Astronomy Without A Telescope – Home Made QuarkGluon Soup  Universe Today

Strings are similar to mesons, where an open string with its endpoints, or ChanPaton factors, are similar to a QCD gluon flux tube with quarks at the end.
Astronomy Without A Telescope – Home Made QuarkGluon Soup  Universe Today

Tevatron managed some heavy ion (gold) collisions at the TeV threshold, created what look like quarkgluon plasmas.

The original concerns were raised by theorists on a "nonzero" possibility that something like a strangelet could assemble from a quarkgluon plasma.
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