It's an exciting time to be a particle physicist.
One of the main reasons, and the focus of this post, is related to the one remaining undiscovered particle of the Standard Model---the Higgs. The Standard Model of particle physics essentially came together during the seventies, making it older than me, and it has passed almost all experimental tests since then. In particular, it predicted the existence of several particles that have since been discovered, including the W and Z bosons and the top quark. But the key to the model, what in many ways defines it, is the Higgs; and this particle will either be found or ruled out by the end of the year. Indeed, the ATLAS and CMS experiments at the Large Hadron Collider both reported possible hints of the Higgs last December.
What is the Higgs? In popular culture, the Higgs is often described as the origin of mass and called the `God Particle'. That name in particular annoys me, and not because I am an atheist; I'd probably like it less if I believed in a deity. The Higgs is nice because it elegantly solves two problems in particle physics, postulating only one new particle. Both of these problems go away if all particles are massless, hence the `origin of mass'. It is worth noting that the Standard Model Higgs is really only one of many possible implementations of the same idea, and the proposal is not without its own problems, but those are topics for another post.
The first problem of the Higgsless Standard Model is the breaking of the electroweak gauge symmetry. A gauge symmetry is a way of rewriting the mathematical content of the theory, without changing the actual physics. A relatively common example relates to the electric potential or Voltage; the only physically meaningful quantity is the difference in Voltage between two points. If you add any constant number to the Voltage at all points, the physics does not change. Gauge symmetries underlie all interactions in the Standard Model, and seem to be necessary for consistency. But they lead to a naive prediction: that the associated force-carrying particles be massless.
The electroweak interaction is responsible for certain types of radioactive decay, perhaps most famously the decay of carbon-14. It was known since the fifties that, if any particles were associated with this interaction, they had to be heavy. In 1983 the W and Z bosons that mediate this interaction where discovered at the SPS collider, also at CERN, and indeed they are eighty to ninety times heavier than a proton. So we have a contradiction: theory predicts these particles are massless, but experimentally they are not.
The solution to this problem is known as spontaneous symmetry breaking, or sometimes the Higgs mechanism. It is named after Peter Higgs, hence the capitalisation. The idea is that the interactions of the W and Z bosons respect the gauge symmetry, but nature "chooses" a vacuum which does not. A chair is a common analogy: the interactions between the atoms making up the chair are the same in all directions, but the chair is not.
There is another way to think about the W and Z mass, that will come in useful in a moment. Consider light travelling through glass; the interactions it has with the glass slows it down (by about 30%). Essentially, the light tries to drag the charged particles in the glass along with it, kind of like dragging a spoon through treacle. For the W and Z, the "glass" is the universe, filled with the Higgs field; the coupling between them leads to the W and Z "dragging" the Higgs field along.
The other problem the Higgs solves relates to the handedness of matter. Consider an electron; this has an intrinsic spin, angular momentum that is not associated with any actual rotation. This is a purely quantum effect, and as such hard to explain; but observations and theory tell us that the spin can only take two forms. If the electron is moving towards us, its spin is either clockwise or anticlockwise (and with a fixed magnitude). If the spin is clockwise, we call the electron "left-handed"; and "right-handed" if anti-clockwise. Only left-handed electrons interact with the W boson.
Except, that cannot be true. Electrons are massive, so they travel below the speed of light. This means that I can always travel faster than an electron. When I do this, the electron's direction of motion (from my perspective) changes, but its spin does not. (This is a good example of when thinking of the electron as actually rotating helps.) This means that if the electron was left-handed before, I now think it is right-handed (and vice versa). In short, the statement that only left-handed electrons couple to the W is observer-dependent.
Note that this is specifically not a problem if the electron is massless; in that case, the electron moves at the speed of light and we can never go faster than it. The fact that the Higgs can also solve this problem is why it was granted its grand title. The way it works is that the coupling of the Higgs field to the electron explicitly changes the handedness. So when the electron gains mass by dragging the Higgs field along with it, it can change from left- to right-handed and back again.
This is my best effort to describe the Higgs in lay terms. There's a lot more to say about it, but at this point I think I'll get onto that in a later post.
 Neutrino masses might constitute a failure, depending on your strict definition of the Standard Model.
 Compare supersymmetry, a popular extension of the Standard Model, which demands at least one hundred new particles exist.
 Strictly, this rewriting should depend on position and time to qualify as a gauge and not global symmetry.
 Not gravity.
 Technically, this is a lie. The electron spin relative to its motion defines its helicity; the chirality is something else, related to the representations of the Lorentz group. However, the distinction would lead us on a long diversion without granting much understanding.