Meaning of "Get it? Got it? Good."

This phrase originated from The Court Jester (link to 2-second clip).

Hubert Hawkins: I'd like to get in, get on with it, get it over with, and get out. Get it?

Ravenhurst: Got it.

Hubert Hawkins: Good.

However, I have seen it being used as a phrase—"Get it? Got it? Good" (example on YouTube).

What does it mean as a phrase said by one individual, and what are some examples of when one would use this phrase?

It all depends on where you put question marks and exclamation marks (or fullstops).

You can have all the four combinations: interrogative-affirmative, interrogative-interrogative, affirmative-affirmative, affirmative-interrogative.

The first example, interrogative-affirmative, which requires two persons:

A: Get it? B: Got it. A: Good.

means:

A: Do you understand it? B: I understood it. A: Good (I'm glad).

The youtube example you provided, interrogative-interrogative, requires just one person speaking:

Get it? Got it? Good.

means:

Do you understand it? Did you understand it? Good (I'm glad).

Affirmative-affirmative, requires two persons:

A: Get it. B: Got it. A: Good.

it means:

A: Obtain it (command). B: I obtained it. A: Good.

Affirmative-interrogative, requires one person:

Get it. Got it? Good.

it means:

Obtain it (command). Did you obtain it? Good.

Get It-Got It-Good was a British children's TV quiz show back in 1967, as per that IMDB link.

Here's a written instance from the Radio Times, when it was scheduled after the far better known Jackanory.

It's probably not really worth trying to pin down an exact "meaning" for the collocation. Mostly I'd say it's just a typical "three-part catchy name", similar to, for example, Ready, Steady, Go! (a British pop music show from around the same time).

My answer is only based on the video you posted, as this is the meaning you're after.

He's asking the viewer whether or not they understood what was said. Obviously, a viewer can't respond to a video (even though a lot of children keep trying), so the speaker doesn't wait for an answer from the viewer.

It's similar to "[...], savvy?" (as often said by Captain Jack Sparrow). It is a rhetorical question, implying that the previous statement is important and needs to be remembered.

Note that it's possible to use this in a non-rhetorical sense (when you expect the other person to actually confirm that they understood it), but this is impossible for a Youtube video since you're not having a conversation with the speaker.