I am talking about definite and indefinite articles, and that is not fully correct. As per BillJ's comment:
"This" is a demonstrative determinative functioning as a [definite] determiner.
(the [definite] was later edited out by BillJ)
However, it is my opinion that, while BillJ is correct, I am better off omitting this information. The sole focus of my explanation is the differentiation between definite and indefinite. Whether we're talking about articles or determiners is functionally irrelevant because the differentiation between definite and indefinite remains unchanged.
I am omitting this detail in order to keep the examples simple and understandable. In the scope of my explanation, I am occasionally adding "article" because omitting a noun would require my phrasing to become unnecessarily obtrusive.
"This" is not being used as an indefinite article . It is definitive, because it specifically talks about this woman (not just a woman in general).
(Edit the above is not quite true. Reason 3 is an exception to this)
A woman walked in. (indefinite, it doesn't talk about a specific woman)
The woman walked in. (definite, it is talking about a specific woman)
This woman walked in. (definite, it is talking about a specific woman)
There are three cases in which you can use "this" instead of "the". I think the third case is the correct one for your current example.
Reason 1: I am explaining something and am also using gestures to point out different things.
Let me teach you how to play chess. This piece [points at king] is the king. This piece [points at queen] is the queen. This piece...
It makes more sense when you see the person gesturing. It doesn't really translate well to a written form, because without the gesturing, you don't know how to tell which piece he's talking about.
Unless you of course add his gestures in brackets, which is what I did.
Reason 2: It is used to say that the woman is a specific type of person (usually but not always a stereotype).
I hate arrogant people. I was at work in my shoe store, and this guy walks in, looking at me as if I am his butler.
In this context, this guy is a shortened version of this type of guy. "This type" then refers back to the type of people I was just talking about (arrogant people).
Note: You can also omit the initial statement:
I was at work in my shoe store, and this guy walks in, with a smug look on his face and looking at me as if I am his butler.
Although you never really specified what type of guy walked in, you are still implying that "this" guy is a special type of person, and the rest of your story will explain what type of person he is.
In my example, you can infer that I mean this guy as "this type of arrogant person, who is smug and acts superior".
Reason 3 : A person who up until this points has been indefinite, is now becoming definite.
I was working at the restaurant. There was a woman sitting at a table. This woman was clearly feeling sick. It didn't take long for the woman to sprint to the bathroom and throw up.
Do you notice how the woman, at the start of my story, was indefinite? That is because she was just one of many patrons. But once I started talking about [...] woman clearly feeling sick, I was talking about this specific woman, not just any of the patrons.
This is usually how you start talking about something. You state its existence using an indefinite article ("There was a woman sitting there."). You then refer to them using "this", to indicate that you are now specifically talking about this woman, not a woman ("This woman was feeling sick").
After you have established that, you can use the definite article (the) to continue your story, because you alraedy indicated that "this woman" is the topic of conversation at the moment.
"This woman" then inherently means "the woman I just pointed out".