So, the dust in the ergosphere moves faster than the stuff at the poles, which means it takes longer for it to cross the event horizon. Naturally, a disk forms. With all the dust rushing around the black hole it's not surprising that a little static electricity might build up around the black hole, too. When an electric field moves, it generates a magnetic field. It's just one of those physics things.
Black holes are tremendously powerful, and the field it generates is also powerful.
Electrons that were going to fall into the black hole get caught up in this field. Another physics thing is that, whenever an electric field generates a magnetic field, the force of the magnetic field goes in directions perpendicular to the electric field. Those electrons that move in the magnetic field, they streak out along the axis of rotation, propelled to incredible speeds and energy by the magnetic field. Gamma rays are the highest-power form light can take. The twin jets shooting out from the accretion disk are like insanely huge fountains of light whipped around and away from the black hole.