From experiments we know that particles have some sort of "intrinsic rotation", called spin. This is a fixed characteristic of a particle, just like its mass. Now, it seems that particles with half integer spin (1/2,3/2 etc) are called Fermions and they behave quite differently from particles with integer spin (0,1,2 etc) which are called Bosons. People also say that they behave under different statistics: Bosons don't have any problem being close to each other, while Fermions have big problems with this. This is called the spin-statistics theorem.
An example of Bosons are the force-carriers. Forces are in the quantumformalism described by the exchange of virtual particles, and these particles are bosons. (the reason for this is mathematical, and has to do with the way people introduce these so-called gaugings).
Another example is the meson, which consists of a quark and an antiquark. Quarks are Fermions with spin 1/2, but if you have two quarks together in a bound state you get a Boson (roughly, because 1/2 and 1/2 can only "add up" to an integer).
I hope I was useful, but I'm sure many more people can say something about this :)