What is a Niche?
Niche refers to area in which you would write content or build your website around taking in consideration what your readers(audience) like to read or use. The other terms used alternative to niche are theme or topic. So often you hear from people say "What is the theme of your website?"
A niche focuses on a single aspect rather than a multiple aspects. Or some one can say "It tries to solve a single problem, may be a couple but not a few".
Example, a website about "Take care of your animals" has a much broader scope as opposed to "Take care of you dog" which is more focused on dogs only or "Take care of you German Shepard dog" focuses only on German Shepard dogs. It all depends what area you want to focus and call it as your niche.
Now audience/users who are consumers of this solution would create a niche market. Wikipedia defines Niche Market as
"A niche market is the subset of the market on which a specific product is focusing on; Therefore the market niche defines the specific product features aimed at satisfying specific market needs, as well as the price range, production quality and the demographics that is intended to impact."
Niche is very important and itself can dictate how much your audience can grow, hence your website, so a right Niche selection is very essential step before you begin.