what is the reason why bypass capacitor increases the voltage gain of a circuit?

I have to make assumptions, that there is a bias resistor from the source to ground, and that is what is bypassed with the capacitor.

The source resistor causes a lot of negative feedback which reduces the gain of the circuit. Notice that voltage across the resistor is common to both the input and the output. That means the voltage that the gate sees is reduced by the voltage across the resistor, which reduces the gain.

When you add the bypass cap, for AC the source is at ground potential, and there is no negative feedback, and you get higher gain.

A bypass capacitor does just what it`s name implies. It`s value is selected such that it has an extremely low impedance to the frequency that you wish to amplify. Consequently no ac  voltage is developed across the resistor that you bypass. Any ac voltage developed across the unbypassed source resistor is present at the source terminal of the JFET and is in phase with the input ac voltage applied to the gate and therefore reduces the instantaneous voltage difference between source and gate during the presence of an input  ac voltage. This of course reduces the gain of the amplifier.

You could have verified this with the oscilloscope by comparing the ac voltage across the resistor with the capacitor in the circuit to the ac voltage across the resistor with the capacitor out of the circuit.

Short and simple answer:

The bypass capacitor makes the source resistor look almost like a short circuit to the input AC signal. As a result, the full signal appears across the gate and source.

Without the bypass capacitor, some of the input signal is lost across the source-to-ground resistor. With the bypass capacitor, almost all of the input signal appears across the gate and source.

Only the difference between the gate voltage and the source voltage is amplified.

An amplifier is essentially two different circuits super-imposed. One is the DC circuit that provides power and bias inputs. The other is the AC circuit that provides the actual amplification. The source-to-ground resistor is a needed part of the DC bias circuit but harmful to the AC amplification circuit. The capacitor is nearly invisible to the DC bias circuit but looks almost like a short to the AC gain circuit.