Never seen one working and cannot grasp the concept of operation. Help please ?
Yes, we have used them in physics experiments a lot. Good old days. We have also drawn the characteristics of a triode valve using regular voltmeters and ammeters. Another device was a tangent galvanometer that was useful to measure the charge stored.
They have a rectangular coil of very fine copper wire (they are very difficult to get these days) hanging between the pole pieces of a permanent magnet. Usually a solid cylinder of soft iron is placed that does allow the rectangular coil to rotate about its own axis (usually max 135 deg). The coil is supported by a jewel bearing and a spring (similar to the ones found in mechanical watches).
You can see the diagram and the principle of operation from
https://en.wikipedia.org/wiki/Galvanometer
The spring is very similar to the one used in a balance wheel in a mechanical watch, See a photo in
https://en.wikipedia.org/wiki/Movement_(clockwork)
The galvanometers are basically current devices and the deflection is proportional to the current.
If you want a highly sensitive galvanometer, you hang the coil with a unspun silk fiber and stick a very light mirror (similar to a microscope cover slip, but about 5-8 mm diameter). Set up a optical system that can measure even very small rotation of the coil - often 0.1 to 0.01 degree.
Your toy is a modern device with two such mirrors (coils) mounted at 90 deg with respect to each other. One can scan the x axis and the other can scan the y axis. Instead of plain mirrors, they often use hexagonal mirrors mounted on motors with speed controls.