I had seen the word 'hater' cropping up a lot. It was in rap videos, on urban dictionary (http://www.urbandictionary.com/), and in Facebook comments. But you could tell by the feel of it that it didn't just mean someone who hated.
So I asked my stepson what a hater was. He said "It's someone who hates on you" (with that 'duh' tone of voice that makes it clear that this fact was self-evident). Damn. Thought I was getting to the meaning of 'hater' and I all do is lose touch with the meaning of the verb 'hate'.
So, my back-of-an-envelope definition for 'hater' would be 'someone who dislikes and criticises a particular person or thing'. It's not the same as just 'someone who hates X' because I could hate asparagus or milk but I don't think that makes me a hater.
And what about 'hate on someone'. As a middle-aged Brit I have to say that's not in my personal lexicon at all. I'd be interested to hear from US-based readers about how normal/abnormal the phrase 'hate on' sounds to them.