Is all matter made of virtual particles? This article in New Scientist says that all matter is actually virtual particles popping in and out of existence and nothing more. is this correct?
 A: The terminology "virtual particle" comes from quantum field theory.
Note the third word in QFT, theory. Theory means that it is a mathematical model for calculations which will, if the theory is valid, describe concrete measurements and behaviors  of physical reality. The basic building block of QFT is the Feynman diagram: a mathematical prescription that will give integrals which will describe the cross section and angular distributions and phases in experiments with elementary "particles". By "particles" we refer to the standard model particles assumed to be elementary.

Some of the lines that you see in this image are  called virtual particles and some are called on mass shell particles. The two electron lines are on mass shell, the gamma, the quarks and the gluon are virtual, in this diagram. It is incomplete because although it has as input on mass shell particles, the right side has only virtual ones.
The following decay of a Kaon

shows input real and output real particles, i.e. particles we can measure with our instruments and get their lifetimes, their cross sections etc and check against the theory as exemplified by the Feynman diagrams.
We observe that input is a pair of quarks and output are three pairs of quarks. It is the pairs that are real. The quarks, the gluon, the W exchanged  are virtual, i.e. off mass shell particles: with the quantum numbers from the table of SM particles but an off shell mass.
Now one can say that the K meson is composed of virtual particles if one makes a one to one identification of the guess, a good guess, of how the Kaon is built up, but the Kaon itself is real, as are the pions which are the end products. Real because we measure them with our instruments. Virtual particles are a very useful mathematical tool that simplifies our view of particle interactions, that is all.
In some sense asking about "is everything virtual" is like entering a clock shop with its hundreds of clocks and say " are all clocks  gears". Clocks are made up with gears but are much more than gears. Thus protons are made up with quarks and a sea of gluons, all virtual particles, but a proton is much more than the virtual particles.
Edit: I will incorporate the content of my reply to the comments here.
Electrons  and all leptons are real particles when on the mass shell, i.e. on external Feynman lines. The same is true for photons and Z and W bosons when on mass shell. Quarks and gluons can never be free and measured individually, because of the nature of the strong force. So quarks are always virtual and have to appear in pairs(mesons) or triplets (protons) in the external legs of the diagrams, and it is the pairs and triplets that can be on the mass shell. Gluons cannot be on their mass shell either, and their only externally measured evidence is in hadronic jets.
The nucleus is a more complicated grouping, it contains off the mass shell protons neutrons gluons photons, but all together, the nucleus is on the mass shell  when isolated. When surrounded by electrons it becomes an atom, the atom then is the one that is on the mass shell and contains  electrons +nucleus off the mass shell. When observing a  molecule, the molecule is on the mass shell and contains off mass shell atoms. When observing  a crystal, the whole crystal is on the mass shell and the molecules are off mass shell.
All microscopic quantum mechanically defined items can be sometimes virtual and some times real ( except quarks and gluons which are always virtual). Virtual  is in the contained level and real is the total group that is under measurement and observation.
There is always a real level riding on virtual particles, nuclei, atoms, molecules depending on the magnification one looks at in the microcosm. Our reality rests  on nested levels of virtuality and reality ascertains itself on the level we are examining.
In the classical world we live and move in the underlying levels of virtuality are immaterial, because in addition to the nesting process  described above there is also something called "decoherence"

decoherence is the mechanism by which the classical limit emerges out of a quantum starting point and it determines the location of the quantum-classical boundary. Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the system+environment's wavefunction from interfering with each other.

It statistically transforms all quantum mechanical substructures to the level we measure and describe  with classical physics and certainly call real.
A: Virtual particles exsist for short time. They do not observe conservation of energy. Heisenberg uncertainity principle applies here.
A: Although the New Scientist requires readers to subscribe in order to read the entire article, this is very much the answer I was looking for.  An agreement of 2% of the proton mass with QCD-based calculations is indeed impressive, and a big improvement over previous attempts (and from which I was actually sourcing some of my much less popular responses).
The energy that causes the gluons and quarks to get pumping, dancing, color changing, and whatever else they do, is driven by the relentless popping in and out of existence of other quark-antiquark pairs, as well as other virtual particles.  I'd like to know the details of the analysis they did, but it will need to be published somewhere I don't need to subscribe in order to read.
Although it could not be said when this article was published, the other 2% is no doubt the contribution of the Higgs mechanism with the quarks.  Murray himself should be pleased, as much as figuring out such things seem to have tortured him.
This is a beautiful theory, and it makes a lot more sense than the previous nonsense I read about having "perfect vacuum" in confines of the constantly changing flux tubes.   Now I can finally understand why everyone else at the physics stack exchange is so jazzed about QCD in general.   It makes perfect sense to me now.  Thanks for sharing.
A: New Scientist is a frightfully un science like mag.
the pretend to be science when they are clueless.
"New Scientist says that all matter is actually virtual particles popping in and out of existence and nothing more. is this correct?"
the quick answer is NO.
i will try to give a better answer than that however.
first off, all matter is composed of atoms that are themselves made from subatomic particles.
those subatomic particles are made from quarks in different combinations.
what are quarks made from ? 
string theory says they are made from BRANES (short for membranes) of vibrating strings of energy.
New Scientist should not have used the word "virtual particle" to describe objects with mass, like a proton.
while one can say all matter comes from energy, it is wrong to suggest that the mass you have in your hand will all the sudden pop out of existence.
The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×1034 years.
so the matter that you see and believe to be "real" is not going anywhere.
the term VIRTUAL PARTICLE is best suited for describing force carriers, like how virtual photons mediate the electromagnetic force.
A: a better way to say it would be to say that all matter is created from ENERGY.
the term virtual particle seems to mean something different to everyone.
i have seen folks refer to virtual particles as quantum foam, and i have seen others call virtual particles simply a way to describe field fluctuations.
also beware that many so called "science mags" are clickbait and not real science backed by real experiments.
so, you can think of "solid" matter (things with mass) as being built with elementary particles, that are made up of quarks, that are made up of energy. (vibrating strings of energy is a popular model)
