Traditionally, a tearsheet is a page torn out of a publication showing the work of the photographer or model as published. There are quality tearsheets and worthless tearsheets. Publication in nationally recognized magazines is more prestigious than something in the local supermarket flyer. In deciding what to include as a tearsheet, ask yourself if anyone will care.
With the advent of online media, a common question is "Does being published online count as a tearsheet?". It depends on who you ask. Again, it comes down to recognition. If you are published on www.vogue.com, it's worthwhile to include it as a credit at the minimum. If you are "published" on blog created by a 14 year old called www.hotsexxxxymamas.com, it's probably not good to brag about it.
What about paying to be published? Well if you are stupid enough to fall for that, send me money and I'll publish you on my blog and print it on a 10 year old HP Laserjet printer and send you a copy. All this for a low price of $49.99.