I don't think it is a vibration, it is click feeling, however when do you get the vibration? When you press it or when you place your finger on it. Do you feel this when your iPhone is on your hand or on solid surface like table?
The Home button on your iPhone can detect the presence and pressure of your finger. You can choose between three speeds to provide different levels of feedback when you press.
Choose a Speed option
To change the click feedback when you press the Home button, go to Settings > Accessibility > Home Button and select Default, Slow, Slowest.