As this is an electrostatic influence machine it evidently uses electrostatic influence or induction to generate static electricity.
This electrostatic induction is nothing more than the effect of a charge onto nearby objects without a physical contact. For example, a positive charge will attract a negative charge and repel a positive charge. Therefore, in a conductor, charges will be redistributed as to make the electrostatic potential constant throughout this conductor.
The classic example is an electroscope in the vicinity of (but not in contact with) a charged object.
This is a video of the youtuber RimstarOrg which gives a very good explanation on electroscopes. (he also made a CD wimshurst machine, but mine is esthetically a bit more elegant and requires far less tools)
Most electrostatic machines use inductance to produce a net charge in an object. The simplest version is an electrophorus.
If for example a positive charge is brought near a conductor, it can be seen that this conductor is polarized. (simply said, this positive charge moves all the (negative) electrons a bit towards it. And of course charge x vector is a dipole moment.)
Fig. 1 Conductor in vicinity of charge
One can now ground the end of this conductor which will remove the positive charge located there
Fig. 2 One end is grounded
If one then removes the connection to the ground and the inducing charge, one can see that there is a net negative charge left in the conductor.
Fig. 3 A net charge remains
This is a video of such an electrophorus in action. Check out the channel of this youtuber Thomas Kim. He has all sorts of interesting electrostatic machines made from PET bottles and CDs, he doesn't provide much information, they are probably intended as demonstrations. He also has a CD wimshurst machine. (but mine produces bigger sparks. I did get the Idea of using aluminium tape for the second pair of disks from him.)
A Wimshurst machine and all other electrostatic influence machines are nothing more than elegant, mechanized versions of a sort of double electrophorus.
A Wimshurst machine consists out of two parallel, counter rotating discs with metal strips. The strips pass under so called 'neutralizer' rod which do the separating out of the charges on the strips and the strips also pass under combs which harvest the accumulated charge on the strips.
An excellent explanation of the workings of a Wimshurst machine can be found here:
It is however French, if you know some French, it definitely is worth a read (as it also gives instructions on how to use a Wimshurst machine for electrostatic painting).
The machine I have built is the mirror image of the one explained in that link, so I will give a brief, parallel English explanation.
One can see in the main pictures of this step, that there are 6 different zones on the discs. (and since everything is symmetric, those same 6 zones appear on the other side of the discs)
Even before the discs start spinning, there will be some static charge on the metal strips. Because just touching or handling the disks is enough to charge them a minuscule amount. This charge will amplify itself as the discs are spinning.
For example, the schematic starts in zone 1 with a net negative charge on the back disk strips. The field of this charge induces some polarization of the second disk. In much the same way as Fig. 2
As a front metal strip passes under the front brush of a neutralizer rod, some negative charge gets repelled trough the rod to a strip on the opposite of the disk.
This is similar to Fig. 2 where the "ground" is replaced by an other piece of conductor.
When the contact with the brush of the neutralizer rod is lost, a net positive charge remains on the strip. (If you subtract a negative charge, you're left with a positive charge) Similar to Fig. 3
So, the back disc still has the net negative charge and the (upper) front disk strips now have a positive charge.
Secondly, the front disk strips on the other (bottom) side now have a net negative charge.
Remember that the back disk also turns, but in the opposite direction. In zone 4, the back disk gets in contact with the back neutralizer rod. And the negative charge on the back is produced in exactly the same way as in zone 2.
The positive charge repels the positive charge (or attracts negative charge since it's mainly negative charges that move) on the other side of the disk.
Similarly, zone 5 is the opposite of zone 1 wherein the net positive charge on the front disk polarizes the back disk. As the back disc moves towards zone 4.
Here, the strips of the back disc and the front disc with the same charge pass under a comb-like structure.
As both strips on both disks have the same charge, they repel each other. Secondly the comb acts like a Faraday cage so the charges on the strips desperately want to escape outwards toward the comb. And this is what happens.
The comb does not need a physical contact with the strips as it has conducting points and electric fields towards points are always very strong, so there the air will break down a bit and the resulting ions provide a path for the charge on the strips to escape towards the low potential of the combs. When running a Wimhurst machine, this is visible with a small purple line from one of the points to the disks.
The charge on the combs immediately gets diverted towards Leyden jars where the charge/voltage will build up till there is a spark. (preferrably in a spark gap, or across the strips of the disk) Or, if there are much sharp edges, it will go away in coronas or ionic winds.
Wikipedia has an interesting animated gif that shows everything said previously
in an animation, but it is a bit complicated to deduce how everything works from it and the compact explanation with it.
In theory, the metal strips are not really necessary and this should be possible with only some charge on the surfaces of the disk. A Wimshurst machine without metal strips on the disks is called a Bonetti Machine. But one needs a static electricity generator (for example an ordinary Wimshurst machine) just to start this generator.