The Higgs boson (also known as the Higgs particle) is one of the elementary particles of nature, according to the standard model of particle physics.
The standard model of particle physics is a theory that explains the fundamental sub-atomic particles, as well as three of the four known forces in nature. This theory, constructed mainly in the 1960's and completed by the mid 1970's, was proven to be so successful in predicting the existence and some of the properties of basic particles and their interactions, that it became known as the "standard model". Its mathematical framework is quantum field theory, the theory that emerged as a combination of quantum mechanics and special relativity.
According to the standard model, there are 17 fundamental particles, from which all other particles in the universe are made of. These can be divided into three categories: 6 leptons (electron, muon, tau, and three neutrinos corresponding to these); 6 quarks (called "up", "down", "charm", "strange", "top" and "bottom"), and 5 bosons (photon, W-boson, Z-boson, gluon and Higgs boson). The bosons play a special role in this theory: these particles mediate three of the four fundamental forces of nature. These are the strong force (that "binds" the particles within an atom nuclei together), the weak force (responsible for radioactive decay) and the electro-magnetic force (which is basically responsible for all the other forces we know of, as this is the force that binds molecules together). The 4th fundamental force is gravity, which cannot be explained in the framework of this model (In Einstein's general theory of relativity, it is given a geometrical interpretation). Attempts to unify gravity into the "standard model" are of yet incomplete, and fall within a theory known as "string theory".
The Higgs boson was predicted by Robert Brout, Francois Englert and Peter Higgs in 1964, and was discovered in 2013- nearly 50 years later in CERN. This is the last particle predicted by the model that was discovered, and its discovery completes the experimental proof of the key theoretical predictions of the model.
The Higgs particle has a unique role in the framework of this model. One of the great successes of the model is the unification of the electromagnetic force and the weak force into one force, known as the "electroweak" force. This means that electricity, magnetism, light and some types of radioactivity are all manifestations of a single underlying force (the electroweak force). The basic equations of the unified theory correctly describe the electroweak force and its associated force-carrying particles (the W and Z bosons), except for a major glitch: all of these particles emerge without a mass. While this is true for the photon, we know that the W and Z bosons have mass, nearly 100 times that of a proton. The mechanism proposed by Brout, Englert and Higgs (known, in short, the "Higgs mechanism") is that the W and Z bosons interact with a field that pervades the universe, known as the "Higgs field"; this interaction is what gives them mass. The more a particle interacts with this field, the more massive it is. Photons do not interact with this field, and thus they remain mass-less. Within the framework of quantum field theory, every field has an associated particle, which, in the case of the Higgs field is the Higgs boson. Thus, the Higgs boson is the visible manifestation of the Higgs field, rather like a wave at the surface of the sea.