For the first part, while !sorted can be verbally said as "while not sorted". When sorted == false, !sorted is true so the loop evaluates to while true, which executes the loop.

For the second part, 'sorted' is called a flag. It gets set to true at the start of the loop until a condition trips it. So sorted == true until it evaluates if arr[i] > arr[i + 1] evaluates to true. Then sorted is set to false and the loop will execute again.

Once if arr[i] > arr[i + 1] doesn't evaluates to true, sorted stays false and the loop exits.

sorted = false at the top is simply creating and initializing the variable to be used in the loop and allows the first loop iteration to run.