How does stuttering happen? 

Stuttering tends to happen when there is an interruption in your airflow. Since airflow is the foundation of your speech, an impedance to airflow will affect an impedance in sound. There are two general types of stutters-- a block and a repetition. Blocks occur when the airflow stops at the level of your neck, particularly your vocal folds. When you experience a block, it will feel like you have stopped breathing. This expression is an accurate description of what is happening, as literally, your vocal folds have closed shut, no longer allowing air to come in or come out. Blocks can be obvious to listeners, but can also go unnoticed. Nonetheless, the speaker experiencing the block will feel a buildup of tension and have difficulty restarting their voice. The other kind of stutter is a repetition. This can be repetition of sounds (i.e. b), syllables (i.e. ba), words (i.e. back) and even phrases (i.e. I mean).  In the case of repetitions, the blockage of air is more so inside the mouth, beyond the neck. Due to buildup of tension, the lips or tongue loses control and the outcome is reproductions of the same sound, syllable and word.