Translation:A woman reads.
In casual speak it's normal to say 여자 for girl or woman, but for a language translation, they want you to differentiate between 여자 = woman and 여자아이 = girl.
Also, "은/는" is introducing a new object/person.
"이/가" is using an object/person that has already been mentioned or that both the speaker and listener know about.
Ex: 여자"는" 김치를 먹습니다. "A" girl eats kimchi.
그녀"가" 김치를 좋아하지 않는다. "She" does not like kimchi.
Does this help?
Or maybe it's more like, "The woman, she reads" if you use the topic marker (and "The woman reads" if you use the subject marker).
니다 is how we show that something is happening or is true or does exist. It makes the different between putting together a broken list of words like "me swim" and saying "I am swimming". That's my understanding at least. I have seen better explanations in other comments.
Lady usually refers to nobility though it can be used as a polite term. The Korean word translates best to woman.
With the extra character it is definitely more than one, but in Chinese they often don’t bother to add it, so without that character it can still be plural or singular.
When they say "a woman" they are referring to one woman not many woman,if that was case it would of been "Women read"