Diegetic

Diegetic sound is sound that is directly involved with the scene i.e. sound that would be heard if you were there.

External Diegetic

External diegetic sound is sound that every character in the given environment would be able to hear e.g. A tree falling. External diegetic sound is the most common use of diegetic sound and involves practically all audio that characters can hear:
Environmental Sounds - such as; wind, cars passing, rain, background chatter
Music
Character Speech

These sounds are used to "create the scene" as it immerses the audience within the scene.

Internal Diegetic

Internal diegetic sound is sound that only one character can hear within their mind e.g. an inner monologue. Internal diegetic sound is used less frequently as it is a very situational kind of sound, this means that when it is used, it is used to trigger a certain response from the audience. Types of internal diegetic sound:
Inner Monologue - Used to convey the characters feelings and emotions, used to to get in the mind of the character to 'understand' them
Hallucinations - Used to show signs of mental illness, madness etc.

In this scene of House M.D. the patient begins to hallucinate and the audience can hear and see what the patient is hallucinating, but, all sounds in this scene are internal diegetic as the patient is experiencing all the sounds that are present. 

Non-Diegetic

Non-diegetic sound is sound that is only heard by the viewers (people within the scene wouldn't be able to hear it).

This type of sound is used to add more elements to the scene, such as;
Music - For a multitude of moods: sadness, happiness, remorse etc.
Voice Over (Narration) - Used to add more to the story or clarify certain aspects of the story

The use of narration is heavily used throughout "The Shawshank Redemption" in order to convey the story more fluently.