"tracking cookies" is a term more often applied to cookies that are intended to be accessed by more than one site. A "remember my login on the next visit" really isn't a "tracking" type of cookie, it's just persistent data for that site only.
Advertisers use "tracking cookies" so when they display an ad on one web site and you click on it, they remember that you are interested in that and next time you visit some other site that uses that same advertiser, they can reload your cookie and see your interests and display more "targeted advertisement" based on your known preferences.
Simply visiting a site can count as a "preference". Do a web search for gold watches, and click on the top hits (which are tracked) and that gets you remembered. Or simply visiting a site or a landing page for gold watches, same thing, advertisers remember seeing you on that page even if you don't click anything. Then next time you visit eBay or some other site with the same advertiser on it, they think "well he was looking at gold watches earlier, lets advertise some here too" and so they do.
This is why you will sometimes notice a strange jump in advertisements for a specific kind or class of products from time to time, across a wide variety of web sites you visit - the tracking cookies have been used to decide you have a recent interest in that and are delivering targeted ads to you as a result. "Jeez my cousin was visiting last week and was on my computer looking for watches, and now all these sites I visit regularly won't stop displaying ads for watches!!" And this is why a lot of people don't like tracking cookies.
