You actually didn't fully specify the operation.
Suppose everything starts out with pot at 600 and the led is off.
Now move the pot to 400 for only half a second, and then back up to 600 and remain.
Which of these does the led do?
A. On for 1 sec and then remain off. The downward transition gets detected but not the upward one.
OR
B. On for 1.5 seconds. The downward transition starts 1 sec of led on. Halfway through, the upward transition starts another 1 sec of on.
The implementation depends on what you want to accomplish. You can use the delay() function for A. Changes happening during the delay are lost.
For B you would need to continually read the pot and the millis time in a loop as in Paul's hint. You have state variables "On" and "TimeOfOn" which you set whenever the previous and current values show a desired transition. As you are reading values in loop, if the state is On, you subtract the time difference and, if it is greater than 1 sec, you set the state variable and led to off (0). Within the loop you always set the previous time and pot value to the just measured ones.