It is good to start with some definitions:
What is a Market?
From Wikipedia, "A market is a social arrangement that allows buyers and sellers to discover information and carry out a voluntary exchange of goods or services."
What is a Niche Market?
From Wikipedia, "A niche market is a focused, targetable portion (subset) of a market sector."
So here is an example:
People buying and selling "Computers" is a market. Can we segment and define an even narrower set of people in this market (that is a niche)? Have a look at this:
Computer Monitor - something that is needed with a computer but what type of monitor?
LCD Computer Monitor - a computer monitor that has good picture resolution because it uses LCD technology.
17" Wide Screen LCD Computer Monitor -a specific type of computer monitor that has good picture resolution and shows wide screen DVD's
Sony 17" Wide Screen LCD Computer Monitor - the Sony brand of a specific type of computer monitor that has good picture resolution and shows wide screen DVD's.
Now in the market where people are looking for a computer monitor, there will be a set of people who are specifically looking for a "Sony 17" Wide Screen LCD Computer Monitor" and this is what you would describe as a niche market from a product perspective. It is just a narrow and well defined segment of a much broader market.
For this niche market to make you money, you need to find out are there enough people in the market looking for a "Sony 17" Wide Screen LCD Computer Monitor" and can they afford to buy one. Furthermore, do you have an offer for a "Sony 17" Wide Screen LCD Computer Monitor" that is uneatable compared to the compitetion in the market place and can you communicate this offer to that niche market cost effectively so you can make a profit?
I knew there was a reason why this marketing stuff can be confusing! Alas the 30DCIII will teach you Grasshopper!