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The photograph shows an Induction Coil, or more correctly a Ruhmkorff coil, similar to the one used by Röngen. It is a sort of DC step-up transformer. the primary winding consists of a small number of turns wound around a soft iron core. The secondary has a much larger number of turns of fine, insulated copper wire. the supply to the primary is fed from a battery, in this particular case a 6v accumulator. Current flowing through the primary coil generates a magnetic field, the core becomes magnetized, and attracts the soft iron disk mounted on the spring of the vibrator. When the disk moves forward, the contact is broken, so that the magnetic field collapses, and the disk returns to its original position, completing the circuit once again. The output voltage can be controlled by means of the nickel knob, which alters the frequency of vibration. The output can be further adjusted by changing the ratio of the transformer by means of the switches, shown at the bottom left.    
The power available from a Ruhmkorff coil is limited, and so in due course the high voltage required to energize an X-ray tube was generated by means of a step-up transformer driven from the mains.
These days most X-ray units use a Converter Generator. The mains supply is rectified and used to charge a large capacitor. The DC is chopped up by Solid State Inverter, that does the same sort of job as the mechanical vibrator of the Ruhmkorff coil. The chopped DC is fed to a step-up transformer. The output voltage can be varied by altering the frequency of the inverter.