Niche: With regard to websites, a niche is a topic or subject that a site is focused on. A niche topic is often one that does not have mass appeal and instead is only geared toward a smaller segment of the market.
Some sites are broader than others. For instance, a news website would cover current events, but it may branch out to entertainment and sports in addition to world news and politics. The Huffington Post is a fairly broad website in terms of the topics that it covers, but it has several different niche sections that focus on a particular news topic ("weird" news) or demographic (divorcees).
Newer websites often have an easier time competing in smaller niches or even those that are new or underdeveloped. For example, a site with SEO resources is probably going to have a difficult time competing due to the ever-expanding size of the industry. However, if that website focused on a particular aspect of search engine optimization, like copywriting for SEO, then it would have fewer competitors. As that site grows its brand and increases its own authority on the web, it may be able to branch out beyond that niche market.