When. the pot has a value of >125, the LED will be turn off and then on again - you won't get the full brightness. The brightness will depend on how much time your code takes to run between when it is turned off and when it is turned on. This will not be insignificant, because the map() involves doing an integer division.
There's no reason not to write to the pin each loop unconditionally. It boils down to a write to a memory location (a port), which is pretty fast.
void loop()
{
int potRead = analogRead(potPin); //read input from potentiometer
int potValue = map(potRead,0,1023,0,255); //convert input from potentiometer value between 0 and 255
digitalWrite(ledPin, potValue >= 125 ? HIGH : LOW);
Serial.print(potValue); //print the value of the potentiometer
}
You can avoid having to do the map by comparing against the raw value rather than rescaling the pot value and comparing to a rescaled value. This also means that you keep all the precision in the raw value.
void loop()
{
int potRead = analogRead(potPin); //read input from potentiometer
digitalWrite(ledPin, potRead >= 125*4 ? HIGH : LOW);
Serial.print(potRead); //print the raw value of the potentiometer
}
Avoid magic numbers in your code. Use const variables with meaningful names. The compiler will optimise it down to the same thing as putting the number directly in your code.
const int ON_THRESHOLD = 125 * 4; // *4 because analog inputs are 0-1023
void loop()
{
int potRead = analogRead(potPin); //read input from potentiometer
digitalWrite(ledPin, potRead >= ON_THRESHOLD ? HIGH : LOW);
Serial.print(potRead); //print the raw value of the potentiometer
}