that

In the example above, the speaker uses "that" to refer to the new phrase she learned. Why did she say "that" instead of "it"?

Use "it" to refer to the thing that you're talking about. If you are discussing a new phrase, you can use "it" to ask about the phrase:

A: Hey, what was that you just said?

B: I said "I don't have any beef with him."

A: What does that mean?

B: You mean "have beef"? It's a phrase that means that I'm not angry with him, or I don't have any problem with him.

A: Is it widely used?

On the other hand, "that" is used to refer to something that was not the actual focus of the conversation:

A: I don't have any beef with him, you know? I'm fine with him going out with Renee, as long as he treats her right.

B: "Have any beef"? Is that widely used?

The differences between "that" and "it" are subtle, so it won't cause any big communication problems if you switch them up in the examples given here.

widely (done)

Something that is "widely used" is used by a lot of people. Other phrases where "widely" is used as an adverb to describe a lot of people doing something include:

It's widely available. (A lot of people can get it.)

a widely accepted idea (Something that most people agree is true.)

He's widely known as (something)

a widely held belief (Something that a lot of people believe.)