A boson (named after Satyendra Nath Bose) is one of the two basic types of particles which make up the universe, according to the standard model quantum mechanics (the other is the fermion). They are characterized by having a spin value of some integer, including zero and negative integers (fermions have a spin value of some positive or negative fraction), and not following the Pauli exclusion principle. This means there is no limit to the number of bosons of a particular state in a particular area (every boson in the world could theoretically fit in a single box). Bosons facilitate all exchanges of force (i.e. gravity, electromagnetic, weak nuclear, and strong nuclear), or so the theory goes. In practice, we've not yet seen gravitons, nor explained gluons fully. If you shove your little sister (not that I condone such things) it's bosons (mostly virtual photons emitted by the electrons in your hand) that actually do the pushing.
The fun thing about bosons is that any collection of things which acts sortta like a particle, and whose spins sum to some integer value, will act like a boson. If, for example, you get two electrons traveling together and reduce their temperature sufficiently under the right conditions they will begin to act like a single particle. If one has a spin of +½ and the other has a spin of -½ then the composite "particle" can have a total spin of 0, effectively making it a boson (this special type of boson is called a "Cooper pair"). Fermions bump into each other, bosons do not. Resistance in a wire (as in Ohm's Law) is caused by electrons bumping into each other. If all the electrons form Cooper pairs then this no longer happens, and electricity can flow through a material much better. This is the principle behind superconductivity.
Better yet, bosons can overlap each other with no problem, meaning you can put a bunch of overlapping bosons in a space and they'll act much like one giant particle. This is the principle behind a Bose-Einstein Condensate.