The Higgs Boson is a massive particle that is predicted by the Standard Model of particle physics. However, to date, we have not yet been able to prove experimentally that this particle actually exists: there have been a few indirect pointers toward the particle, but as of yet no conclusive evidence.
If we do discover the Higgs field* then it will probably be one of the most important discoveries of all time. The Higgs is of importance for two reasons: firstly, it completes the standard model of particle physics but secondly (and to a lot of people, more importantly) the Higgs may give us hints as to which is the correct extension of the standard model.
[*Recall that, in field theory, particles and fields are taken as synonyms.]
I'll focus on the second point in this discussion. String theory is, in the scientific world, the theory with most backing to be the correct extension to the standard model. Of course, this by no stretch of the imagination means that it is correct! String theory seems to require that the world in which we live exhibits a phenomenon called supersymmetry (SUSY). The relevance between this theory and the Higgs is that an extension of the standard model, with string theoretic boundary conditions contains Higgs bosons. Thus, if we find the Higgs, this strongly supports the supersymmetric extension of the standard model, which in turn supports the notion that string theory is the correct theory of nature. However, I should point out that, if we don't find the Higgs, then the story isn't over for string theory; there are versions which do not exhibit SUSY.
So, what are we doing to try and find this elusive particle? Well, as I mentioned in another thread, the LHC at CERN is due to switch on sometime in 2008. This particle accelerator has a strong probability of being able to detect the Higgs. Thus, by this time next year, we could be a lot more knowledgeable about the physics governing the world in which we live.
~neutralino
If you haven't found something strange during the day, it hasn't been much of a day - John A. Wheeler.