The latest xkcd comic led me to read about the Kardashev scale on Wikipedia, which is one of these wonderfully pointless ideas (such as the Drake equation) dreamt up by people who I'm sure, like me, read a lot of science fiction as children, and are consequently fascinated by the idea of extra-terrestrial life and ultra-advanced civilisations. But that's not what I want to discuss here. The article mentions anti-matter, and this is a concept which is often misunderstood by non-physicists.
So what is anti-matter? Our world is made up of particles — the stuff around you is made of atoms, which in turn are made up of electrons and atomic nuclei. Electrons seem to be pointlike, while the nuclei are ultimately made up of other seemingly pointlike particles called quarks and gluons. Quantum field theory, which represents our current best understanding of how the universe works on the fundamental level, tells us that for every type of particle, there is also an anti-particle. It has exactly the same mass as its corresponding particle, and the same spin (a number which measures how fast a particle rotates, in a technical, quantum mechanics sense!), but the opposite charge. For example an anti-electron, which is usally called a 'positron', is identical to an electron in every respect, but has a positive electric charge instead of a negative one. A similar statement holds for all anti-particles — they are exactly the same as the corresponding particle, except for their charge. Note that we actually know about more types of charge than just ordinary electric charge, such as the 'charge' carried by quarks which holds them together to form protons and neutrons. All of these charges are reversed for an anti-particle.
In fact, since what we call 'positive' and 'negative' charge is just a convention, the only real difference between matter and anti-matter is that our universe contains a lot of matter, but almost no anti-matter. Why is that, you ask? That's a good question. In fact, it's such a good question that nobody knows the answer!
In newspaper articles and other places, one sometimes reads that when matter and anti-matter meet, they "turn into pure energy", or some similar nonsense. I say nonsense, because there is no such thing as 'pure energy' (see below for a caveat to this statement). So what does happen when, say, an electron and a positron annihilate? Their energy is typically carried away by photons — particles of light. Photons are somewhat special — because they don't have any charge at all, an anti-photon is exactly the same as a photon. Sometimes we say the photon is its own anti-particle. But although they don't have charge, photons do carry momentum and angular momentum, and if you carefully measure this, it can tell you about the momentum and spin of the original electron and positron. You certainly wouldn't know anything about those quantities if I just told you the total energy of the pair of particles! The lesson is that energy is always carried by something; there is no such thing as 'energy' in the absence of any particle to carry it. A related issue is the apparent widespread misunderstanding of what Einstein's famous equation E = m c^2 actually means, but I might write about this another time.
For now, I want to leave you with some exciting semi-recent news about anti-matter. Because anti-matter behaves exactly the same way as ordinary matter, it can also form atoms, the simplest of which is anti-hydrogen. Until recently, scientists could produce anti-hydrogen, but only keep it trapped for a fraction of a second before it annihilated with some ordinary matter. Earlier this year, however, the ALPHA experiment at CERN (where the LHC is currently doing its stuff, but that's not all that happens there) released a paper in which they announced that they had successfully trapped atoms of anti-hydrogen for up to fifteen minutes or so. This will allow them to study, for the first time, detailed properties like the energy levels, to test whether these really are exactly the same as for ordinary hydrogen, as theory predicts. For the cognescenti among you, this is a consequence of CPT invariance, which holds in any Lorentz-invariant quantum field theory.
(I said earlier that there was a caveat to my statement that there is no such thing as pure energy. In fact, Einstein's theory of general relativity allows space itself to have a non-zero energy density — this is often referred to as the 'cosmological constant' for historical reasons. This energy is uniformly spread throughout space, and does not have any associated momentum. A constant energy density like this certainly cannot arise from the annihilation of two particles of matter and anti-matter, which is why it was not relevant above.)