So... What is a Niche?
The easiest way to describe a niche is that it is a topic that you can build your website around. For example, someone might have a website about 'Food', which is a very broad topic. This might be a popular topic, but is going to have a LOT of competition, often so much so that unless they have a massive advertising budget, they will never get more than a few interested visitors a year.
If this person was to focus on a particular type of food, say... 'Chocolate Ice-cream Recipes' they can make their site the foremost authority on chocolate ice-cream recipes, with much less effort than it would to get recognized for a generic 'food' website.