The question is in the title.
A bit of background info: the escape velocity at the photosphere of the Sun is ~ 620 km/s, but the mean speed of the solar plasma there (inferred from the temperature) is ~ 150 km/s.
Yet not only is the solar wind able to escape the surface, reaching out to ~ 100 a.u., but it's speed there remains relatively high and constant (as Voyager 2 shows, until ~ 85 a.u. the speed is about 400 km/s:
So basically it seems the wind gets almost twice the energy needed to escape (the half of which is spent to actually escape, and the other half remains in the form of kinetic energy) "out of nowhere".
I have read that the extra energy is supposed to somehow come from the magnetic field. How exactly? And why at the same time it does not seem that the magnetic field of interstellar plasma is attenuated because of that?