가 (이 after a consonant) marks the subject of a Korean sentence. Subjects are new information, things which appear for the first time.
이분이 누구예요? Who is that person?
We don’t know, as we have never come across him before. New information.
Korean sentences may also have topics marked by 는 (은 after a consonant). A topic is old information, what we know already. 는 may follow several other particles meaning e.g. in, at, by, to, from and bring the phrase created to the beginning of the sentence. This will be explained in detail when these particles come up in the conversations.
When the topic is the subject or object of the sentence, 가 and 를 (the object marker, 울 after a consonant) get deleted. Because a phrase with 는 is old information, it may be presumed that it is already known and so the whole phrase is likely to be dropped:
(in response to the question above) (그 사람은) 마크예요. He’s Mark.
I know who he is, and he is no longer new information.
는 may also indicate a contrast. In this use it may actually indicate old information which is being contrasted, and does not need to come at the beginning of the sentence:
안나 씨는 학생이에요. 저는 회사원이에요. Anna is a student. I am an employee.
서울 날씨는 더워요. 하지만 런던 날씨는 추워요. Seoul’s weather is hot. However, London’s weather is cold.
In this contrastive function, one often sees two 는s, as above. It's also possible to get only one: 파리 날씨는? What about Paris's weather?
Note that 아니다 and 되다 are usually preceded by the particle 가 (이after a consonant):
저는 학생이 아니에요. I’m not a student.
저는 대학생이 돼요. I’m becoming a university student.