ta dziewczynka most literally means "this girl", but it can also mean "that girl" or "the girl" if that fits the English sentence better.
Since Polish does not have articles, there is no difference between a girl and the girl, if that difference needs to be highligthened we use the girl=this girl , a girl=some girl
Google Translate is not really a reliable source of knowledge.
But well, it's right here, all of those translate to 'this', this is a distinction that's not present in English.
The determiner has to agree grammatically with the noun it describes in terms of number, gender and case. Right now you've probably only seen Nominative - the basic case, the 'dictionary' one, used mostly for the subject of the sentence. So in Nominative singular you will have "ten" (for masculine nouns), "ta" (for feminine ones) and "to" (neuter).