You could say that your niche is a combination of the target audience your site will cater to along with the products/services they would prefer. So that you would be promoting, urging them, to avail of those products/services.
niche can also be said to be like if you have a special quality or something.like he has created a niche for himself in the field of art.it can be used in various forms.you can also google it if you are looking for the perfect answer.
All these comments are great. I would just add that if you are looking to find your niche social media marketing can help you accurately find exactly the people you want to speak to. Pushing your message out to social media sites like Facebook and Twitter will help you gain more authority within your niche.