Entering three of the four values for Vin, I, Vf, and R calculates the missing value.
The brightness of an LED is dependent on the current flow through it. The voltage drop (Vf) across the LED will vary with the color of the LED as well as the current flow. When using the LED as an indicator, as opposed to a light source, a current of 5mA to 10mA is normally sufficient. For that current level, reasonably good values for Vf based on color are:
Rather rely on the values listed above, you should consult the data sheet for the LED and select the value of Vf for the current level you are interested in.
The solver calculates the resistance value by finding the voltage drop across it, which is Vin - Vf, and then using Ohm’s Law to and the specified current level to determine the resistance. Other values are calculated in a similar way recognizing that the voltage drop across the resistor is Vin - Vf and applying Ohm’s Law to determine the missing value.