What is antimatter? Can you give a visual example of what is antimatter?
With the re-opening of Large Haldron Collider scheduled in Mar 2015, I'm reading that they smash two particles together to try to re-create particles that might have been there are the beginning of the Big Bang, and this includes antimatter?
Is antimatter something we can see, or it is some invisible field. I'm trying to get my arms around this concept.
 A: To complete the good answer by Photonic, one should add that antimatter has been observed in the laboratories and experimented with for over 60 years, in terms of individual antimatter particles. It is also continually created by cosmic rays impinging on our atmosphere.
The easiest to create in the lab and the atmosphere are positrons because of their small mass.


This bubble-chamber event shows the creation of a positron-electron pair (the linked spirals) by a photon in the Coulomb field of an electron. The electron is ejected from the atom and creates the third track that connects to the two spirals. After about 1 cm the single electron emits a gamma ray, which then converts into an electron-positron pair with straighter tracks. (Lawrence Berkeley Laboratory.)

The little spirals on the beam tracks going through are electrons ejected by an interaction with the incoming beam with a bit more energy than the ionisation electrons that make up the dots that show the tracks of charged particles through the bubble chamber.
The LEP collider was colliding electrons with antielectrons (positrons) and studied what happened.  . 
Antiprotons were created in the 50's 


An antiproton (blue) enters a bubble chamber from bottom left and strikes a proton. The released energy creates four positive pions (red) and four negative pions (green). The yellow streak at the far right is a muon, a decay product of the adjacent pion. (The dark blue curlicues are low-energy electrons knocked from atoms, not involved with the antiproton.) 

They have even created anti hydrogen 
The problem with bulk antimatter is containment, as any container will necessarily be of matter, thus they can only be contained with magnetic fields and studied with sophisticated methods , as with antihydrogen.
A: Antimatter is simply matter with an opposite charge in each particle. It will (probably) look and behave exactly the same as regular matter.
However, no one has made enough antimatter to actually test that it does look the same. The major obstacles are the energy cost and the handling problems. Antimatter has to be built up from pure energy, and the stuff has the nasty habit of exploding violently when it contacts regular matter. The Hiroshima bomb turned about 700 milligrams of matter into energy, you could do the same thing with 350 milligrams of antimatter - that's a ball of anti-iron about 5mm across. Even the tiniest leak in your containment device will result in your lab, and anything else within a kilometer, simply disappearing.
A: Paul Dirac in the 1930's described a vacuum as not empty space but as an infinite sea of negative energy particles. 
His famous 'Dirac Equation' has a negative energy solution for the electron, he interpreted this solution by saying that since Pauli's Exclusion Principle states that 'no two electrons (fermions with half-spin) can occupy the same quantum states', all of the negative energy states below the ground state predicted by his equation must already be occupied by particles, say for examples electrons.
Now, if you imagine a gamma ray photon transforming via pair production into an electron and a positron, you can think of the positron as a hole in this infinite sea of negative energy which is what Physicists detect as being an antimatter particle, with the same mass, spin etc as its matter counterpart, the electron, but opposite sign on its charge. 
Below is a visual representation of this;

I wouldn't take this way of thinking of antimatter too literally, however I find it to be a useful way of picturing the essence of antimatter. 
Hope this helps. 
A: Antimatter is the 'quantum opposite' of matter. An electron, which is a particle of matter, will have an 'opposite partner' which we named the positron. The positron has the same mass as the electron, but has opposite electrical charge, i.e +1.
But antimatter does not only distinguish between electric charge. Antiparticles in general have opposite quantum numbers which are namely:


*

*Electric charge

*Colour Charge

*Flavour number

*Lepton number

*Baryon number

*Isospin


and others which I'm probably forgetting. This makes the behaviour of antimatter to 'reflect' that of its matter partner. For example both the electron and the positron travelling along the x-direction will react to an external magnetic field along the y-direction. The only difference would be the direction of the force, which will be opposite as seen in the picture below:

It is worth stating that the laws of physics are not completely symmetrical when we make the change from matter $\to$ antimatter. In the early universe, right after the Big Bang, equal amount of matter and antimatter was created. Matter and antimatter annihilates each other and produces photons. For that reason there should be no matter nor antimatter in our universe. All matter should have annihilated all antimatter in the early universe, but that clearly did not happen because here we are (sitting on a 'matter chair' drinking 'matter coffee') asking this question. 
So there clearly is an asymmetry. Where does it come from? Well, asymmetries have been observed between matter and antimatter, mainly in weak decays, where it has been shown that C-symmetry violation occurs. Particles change to antiparticles when acted upon by the Charge conjugation operator
$$ {\mathcal C}\,\lvert \psi \rangle =\lvert{\bar {\psi }}\rangle $$
Notice that chirality remains unchanged by $\mathcal C$. Consider the example of a left-handed neutrino under $\mathcal C$-conjugation. It becomes a left-handed anti-neutrino, which is well-known not to participate in the weak interaction at all. It was then thought that physics laws would definitely be symmetric under both charge conjugation and parity inversion, which just switches a particles position in space, i.e:
$$ {\mathbf {P}}:{\begin{pmatrix}x\\y\\z\end{pmatrix}}\mapsto {\begin{pmatrix}-x\\-y\\-z\end{pmatrix}} $$
Together, they form the combined $CP$ transformation. In principle, $CP$-symmetry should be conserved, i.e physics should be the same if we exchange a particle for its antiparticle, and invert its coordinates, but this symmetry was also found to be violated as well. This is one possible origin for the asymmetry between matter and antimatter, but this alone is not enough to explain the huge difference of matter vs antimatter in the universe hence why the question is an open research question.
