Translation:A woman is a woman.
Formality is related to Korean culture. It's common in eastern culture.
For example you talk in an office meeting, you have to use formal sentence. But if you speak with your friends just use an informal sentence.
는 (neun) is topic marking particle. Not many languages use it. Mostly it is the subject of the sentence in other languages (but it is not always). For beginner just get to use it.
FYI, subject marking particle in Korean use 이/가.
은/는 is a topic marker. I think of it as "speaking of.../about...".
So 여자는 여자입니다, could be like "speaking of woman, it is/they are a woman". Something like that.
은 is used if the previous syllable ends in a consonant. Example: 연필은," speaking of pencil..."
는 is used following a vowel like the example 여자는, "speaking of women"
I'm still learning a lot too, so any corrections are appreciated!!
I personally did not use this website to learn but it has explanations of topic vs subject particles here: http://www.sayjack.com/blog/2010/06/07/korean-topic-particle-and-subject-particle/
also here tells you what particles do, there's also links below to other things Duolingo covered so far; like "and" and "or": http://www.sayjack.com/blog/2010/06/06/introduction-to-korean-particles/
Ok guys u CANNOT learn the basics here. Basically its for those who already knows....can u please find a website that can teach u? I'll recommend busyatom.com......it starts from the alphabet >verb endings>sentence structure>conversations etc.....it is actually a video that u watch and listen to. You should have a notebook to take notes as well.
Ok..... I dont know half of the stuff, and i just learned my abc's 3 days ago. But some words do sound the same in my languages Spanish/English. Some to me are just common sense like Bread, in Korean I hear Pam in spanish is Pan. And if you want to know the basics download Write It! Korean. I literally learned them in one day. They only have the abc but trully awsome and you catch everything right away even how to properly stroke.
I agree with Laure that DL could have been a wee bit more creative in sentence selection.
davideventu1 makes a great suggestion re: http://www.howtostudykorean.com
If you are looking for Korean sources on the web, check out this post for a long list.https://www.duolingo.com/comment/23695875
https://www.duolingo.com/comment/24915626 provides links to the 이/가 , 은/는 issue.
https://www.youtube.com/watch?v=r4TNuJYeJM8 is a tad more advanced than our current level, but presents a great overview of 8 basic verb endings, and different levels of formality, including -ㅂ니다. It is one of "Talk to Me in Korean"'s many free videos available on the web.