I assume you're talking about a
CRT oscilloscope.
Around the
CRT, there are two sets of coils, the deflection coils. The horizontal coils are driven by the sweep generator, the vertical coils are driven by a preamplifier of some sort that modulates the
voltage to the coil based on the input (the signal to be displayed). The magnetic field created by the deflection coils will impose a force upon a charged particle, in this case electrons, emitted by the electron gun.
The electron gun is located at the back end of the
CRT. By thermionic emission, it emits electrons which are accelerated by a
potential difference, often of several thousand volts. These electrons travel to the other end of the tube, and depending on the
voltage and hence the magnetic field created by the deflection coils, will
strike the
screen in a certain place.
The
screen is coated on the inside with a certain phosphor, a coating that emits light when struck by electrons.
The horizontal deflection coils are driven by the sweep generator, which can either produce its own sweep signals, derive them from the AC
line, or optionally from another source. These coils move the beam of electrons sideways, across the
screen.
The vertical deflection coils are driven by the input
amplifier. They move the beam of electrons up and down.
Multi-trace oscilloscopes operate the same way, except for the fact that the traces are multiplexed in some way. There are two ways that I know of. The first is to display the signals sequentially, but applying a DC
bias to each successive signal so it appears on the
screen above or below another.
The other method is to rapidly
switch back and forth between the two signals, at such a frequency that the switching is not visible to the eye.
The first oscilloscopes used vacuum tubes, requiring extra rails from the
power supply, as well as regular maintenance when the filaments burned out. The (relatively) few
CRT oscilloscopes still in production use solid-state components.
The result of this is that the signal appears on the
screen, in a graph of
voltage with respect to time, or if the
unit is set differently, with a different
voltage.