From what I understand the term comes from print media, such as magazines and papers, which send copies of the puplication to contributors as proof of the inclusion of their work. A tearsheet simplifies this by being a single page 'torn' from the publication -- that is, instead of sending a partial page ad sponsor a full copy of a magazine, the publisher would send them just the page their ad runs on.
More broadly, in resumes, portfolios and such, a tearsheet would become a single sheet that focuses on a very specific item -- such as a single photo with description and comentary.
My understanding may be wrong, but I was unable to find a more definitive definition.
Tear sheets can also be a conversation starter when shooting a portrait or fashion photography. Having people bring in photographs "torn" from magazines or other places gives the photographer and client something to talk about in terms of what they like, don't like, clothing, lighting, props, etc...
