Other than being the possessive particle, の can have a lot of other meanings. (see sticky particle post)
In this case, I think it expresses emphasis (or "speaker's feeling" so as to say).
Written form is の
Verbal form is usually pronounced as ん
e.g.
学校へ行きます。(normal polite form)
rough english translation : "(I am) going to school."
学校へ行く. (casual form)
rough english translation : "(I am) going to school."
学校へ行くの。(emphasis on speaker's part. often found as response to question too)
(verbal: 学校へ行くん。)
rough english translation : "(I am) going to school!!!!!"
This is also often found in questions:
e.g. 学校へ行くの。 (can be statement or question if pronounced like question. hard to explain here, but when you get the hang of it, you will know when somebody meant a statement as a question or otherwise)
rough english translation : "(are you) going to school????????"
In context (imagine this made up phone conversation on a Sunday)
A: 今日は映画どう.
B: 悪い。今学校へ。
A: 日曜日なのに。学校へ行くの.
B: ええ。ちょっと用事があるの.
rough translation
A: How about movie today?
B: Sorry, I am going to school now.
A: It's a Sunday! You are going to school????
B: yup. There are some matters (to attend to).
May not be directly related, but another common use of の is as a shorthand for こと.
I am not sure whether the case I mentioned above is really a common-use case of こと, though. e.g. 学校へ行くの。 -> 学校へ行くこと.
Experts out there, please correct me if I'm wrong