Lajocar explained this well. However, I would like to add that a niche is a group of people who are very interested in a
specific topic within a market. Going off the examples that Lajocar brought up...
Within the diapers market, there are several niches: parents who want to buy organic diapers, parents who want to use re-washable diapers, diaper allergies (i dunno if this exists or not, but just an example

), etc.
Examples of niches in the "Musical Instruments" market: left-handed guitars, learning how to take care of your guitar, etc.
In my opinion, the more specific the group is, the better off you will be able to address that group's needs, questions, and concerns. Also, another important thing to think about is how to add value to the people within the niche you choose, i.e. consider how people within the niche will benefit from your website.
I hope this helps.
Sherif