If you know what a Bohr magneton is, a nuclear magneton is the same thing, except using the mass of a paroton instead of the mass of an electron. Specifically it is defined by \mu_N=e hbar/M_p, with the numerical value \mu_N=3.15X10^-14 MeV. It arises from the connection betrween angular momentum and magnetic moment. Using the Dirac equation, the magnetic moment of a spin 1/2 particle proton would be given by \mu_p=\mu_N. But the proton has an anomaloous magnetic moment so that its actual value is \mu_p=g\mu_N, where g is called the "g value" or more commonly nowadays g is called "the magnetic moment" given in units olf the nuclear magneton, \mu_N.
This is what is meant by the statement "The magnetic moment of the proton is 2.79", because that is the value of g for the proton.
The nuclear magneton is just a convenient unit in which to express magnetic mooments of hadrons.