Everyone may have their own definition of a Niche market, but I'll share mine.
I consider a Niche market, to be one where there is a need for a product, but supply does not outsrip demand. Now that's a very broad description, but that's my definition in a nutshell, but typically a Niche is a specific segment amongst a much larger market.
For example, you mention school supplies. School shoes on their own is considered a primary market, but perhaps there is a style of shoe, a colour or even a brand that is more popular among kids than others, but that hasn't yet been discovered by sellers as yet and so that is then a Niche.
Some Niche's stay Niches because the demand for the product isn't great enough to encourage sellers to waste their time, sales are just too slow to worry about it and then others don't stay Niches for long because once discovered, others then storm into the market and flood it to the point where supply outstrips demand and then you have a saturated market, the very opposite to a Niche.
So Niche markets aren't always easy to find, if they were, then everyone would be dealing in them for the most part. How do you find them, you have to drill down through products, just as I used for me example with the school shoes. Perhaps there is no Niche to be found in colour, style or brand, perhaps you have to drill down further to the shoe laces, maybe chrams that hang fro the laces and so on.
There's never any guranatee of finding a Niche, but they take a lot of effort in searching for them unfortunatley. That said, if you do find one, then all that looking can pay of for you.