What makes the connection?

Usually, it's capacitive coupling.

Could you explain further, please, Timur?

Yes, I can.

A capacitor is a device that stores energy (electricity).

Behind the screen glass there's a capacitors array.

When you approach your finger you modify the capacitance, hence the flow of energy.

The trajectory of your finger is detected by the capacitors change and the processor infers the subsequent actions : modifications of the display.

When you press your finger more onto the screen, you increase the area affected by the capacitor's change.

You get the impression that you obtain more reactions as you press more, which is not the case, it's the increase of the area.

Wrapping your finger in a t-shirt diminishes the capacitance, hence the difficulty to obtain the same fluid movement..

Thank you very much, Timur. Does heat have anything to do with it or is it only pressure? Would an ice cube cause any/the same response?

My pleasure.

For practical purposes, it has nothing to do with heat.

However, according to the fundamental laws of physics, temperature has a slight effect by ways of dilatation.

A raise in temperature will increase the capacitors area but also increase the resistance to the flow.

That's why super computers technology uses superconductivity, which, as you know, is produced at very low temperatures.