The sketch TestServoSpeed increments the value of a variable named pulseWidth by 25 each time through a for loop.

  // Loop counts with pulseWidth from 1375 to 1625 in increments of 25.

  for(int pulseWidth = 1375; pulseWidth <= 1625; pulseWidth += 25)

With each repetition of the for loop, it displays the value of the next pulse width that it will send to the pin 13 servo, along with a user prompt.

    Serial.print("pulseWidth = ");           // Display pulseWidth value
    Serial.println(pulseWidth);
    Serial.println("Press a key and click"); // User prompt
    Serial.println("Send to start servo...");

After Serial.begin in the setup loop, the Arduino sets aside some memory for characters coming in from the Serial Monitor.  This memory is typically called a serial buffer, and that’s where ASCII values from the Serial Monitor are stored.  Each time you use Serial.read to get a character from the buffer, the Arduino subtracts 1 from the number of characters waiting in the buffer. 

A call to Serial.available will tell you how many characters are in the buffer.  This sketch uses while(Serial.available() = = 0) to wait until the Serial Monitor sends a character.  Before moving on to run the servos, it uses Serial.read( ) to remove the character from the buffer.  The sketch could have used int myVar = Serial.read( ) to copy the character to a variable.  Since the code isn’t using the character’s value to make decisions, it just calls Serial.read, but doesn’t copy the result anywhere.  The important part is that it needs to clear the buffer so that Serial.available( ) returns zero next time through the loop.  

while(Serial.available() == 0);      // Wait for character
Serial.read();                       // Clear character

Where is the while loop’s code block?
The C language allows the while loop to use an empty code block, in this case to wait there until it receives a character.  When you type a character into the Serial Monitor, Serial.available returns 1 instead of 0, so the while loop lets the sketch move on to the next statement.  Serial.read removes that character you typed from the Arduino’s serial buffer to make sure that Serial.available returns 0 next time through the loop.   You could have typed this empty while loop other ways:
   while(Serial.available() == 0) {}  
...or:
   while(Serial.available() == 0) {}; .

After the Arduino receives a character from the keyboard, it displays the “Running…” message and then makes the servo turn for 6 seconds.  Remember that the for loop this code is in starts the pulseWidth variable at 1375 and adds 25 to it with each repetition.  So, the first time through the loop, servoLeft is 1375, the second time through it’s 1400, and so on all the way up to 1625. 

Each time through the loop, servoLeft.writeMicroseconds(pulseWidth) uses the value that pulseWidth stores to set servo speed.  That’s how it updates the servo’s speed each time you send a character to the Arduino with the Serial Monitor.

Serial.println("Running...");
servoLeft.writeMicroseconds(pulseWidth); // Pin 13 speed=pulse
delay(6000);                             // ..for 6 seconds
servoLeft.writeMicroseconds(1500);       // Pin 13 speed=stop