In Turkish there is a root word and suffixes are added to build more complex ones. In this case iyi, the root, is used as a verb and the subject of the sentence is added as a suffix. As such in oral conversation the subject pronouns are often not needed (kind of like Spanish)
Ben iyiyim - I am fine
Sen iyisin - You are fine
O iyi/iyidir - He/She/It is fine
Biz iyiyiz - We are fine
Siz iyisiniz - You are fine
Onlar iyiler/iyidirler - They are fine
I hope this helps.
In English, we might say "it's fine" where "it" is kind of semantically empty to say "the situation is fine" or, more figuratively, "don't worry about it."
...Can you say "O iyi" in the same way to mean "it's fine" like you would in English? Or would the "O" be emphatic (e.g., "HE/SHE/IT is fine"), so you could just say "iyi"?
Edit: Some googling makes me think that the equivalent of "it's fine" is "gerek yok."