A monitor needs 30,000 volts to accelerate electons within the picture tube.
At the back of the tube, is a hot filament (not as hot as a light bulb, but hot enough to glow). The heat causes electrons to 'evaporate' off the filament, where the form a cloud around the filament.
Because electrons are negatively charged, and because opposite electrical potentials attract, a positive voltage (compared to the voltage at the filament) will attract the electrons. In a picture tube, the positive electrode is about half-way along the tube.
By applying a high voltage to this electrode, electrons will be attracted towards it, and start accelerating towards the front of the screen. The electrode is arranged in such a way that the electrons don't actually hit it, but carry on straight past it, so that they smash into the front of the tube. The front of the tube is coated in phosphors, which will glow when hit by the electrons.