Protons, electrons and most other particles have intrinsic spin, a form of built in angular momentum (just like it sounds). But "fermions", a class of particles that includes protons and electrons, have spin that is one half of Planck's quantum of angular momentum, and this property is connected with several other differences between fermions and bosons (particles with integer spin). One of these is the Pauli Exclusion Principle, which says no two fermions can be in the same state in the same place at the same time -- in contrast to bosons, which (like idiots everywhere) love to be in the same state!

If that answer is far more complicated and confusing than you wanted or expected, join the club. Except for a few "natural philosophers", most physics students look upon this division of particles into half-integer-spin fermions and integer- (or zero-) spin bosons as a fact of nature that we can't "explain" but simply have to "get used to".