Via thermionic emission the heated hot cathode generates a cloud of electrons.
The filament voltage heats the hot cathode so there thermionic emission of electrons is possible.
The high voltage between cathode and anode charges the anode positive. So the electric field accelerates the electrons in the direction of the anode.
The Wehnelt cylinder focuses the beam. It is charged negative and so the electric field focuses the electron beam in the middle.
The glass tube is evacuated so the electrons do not interact with other particle or atoms.
When filament voltage and acceleration voltage are on the electron gun generates a fine beam of fast electrons. This beam is not visible to the unaided eye.
The acceleration voltage generates an electric field between hot cathode and anode. This field accelerates the electrons in the direction of the anode.