We describe electroweak theory by $SU(2)_L\times U(1)_Y$. This group has four generators which will be the W's, Z and $\gamma$ and we get 4 associated currents. We complexify the first 2 generators of SU(2) to describe the charged W bosons.
$\sigma^\pm = \frac{1}{\sqrt{2}} (\sigma_1\pm i\sigma_2)$ And then the charged current is $J^\pm \propto \bar{\psi}\sigma^\pm\gamma_\mu\psi$, which are the charged currents describing the W bosons. The remaining SU(2) generator and the U(1) generator form the neutral currents of the Z and $\gamma$.
Why are the complexified currents now charged currents and the remaining two said to be neutral? Why is it a charged current now that it we complexify it? and how come a minus and a plus sign for the complex number changes the charge of the current/boson