This experiment is a circuit configuration of an oscillator called Astable Multivibrator. In this type of oscillator there is no inductor, the frequency is controlled only by the resistors and capacitors. One of the two transistors is always on, hence one LED is always on. The left transistor (left-LED) is controlled by the 100k ohm resistor and 10 microfarad capacitor. The right transistor (right-LED) is controlled by a 3.3k ohm resistor, variable resistor (0-50k ohm), and 100 microfarad capacitor. If the variable resistor is turned up to 50k ohms, the right LED will stay on longer than the left one. Because the capacitor's discharge time is being manipulated, with the variable resistor.
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