Many articles published in scholarly journals and popular (general interest) magazines are not freely available on the web (although they may appear that way).
The library is purchasing subscriptions to these journals so that students and faculty will have access to the articles even when they are simply searching the web. (Google sees the Cornell IP address and provides access through the Cornell Library subscription).
This doesn't work for every article reference you find on the web (even when the library is subscribing to the journal) and it never works for other types of publications.
What can you do? Use the library's journal databases.
Who published the article? Is it published within a journal, a magazine for the general public, or was it an article intended to drive business to a dot.com website?
Is the journal peer-reviewed?
There's lots of discussion about the pros and cons of peer-review these days, but selecting from peer-reviewed articles is one way for you, as a student, to identify scholarly publications.
What are the author's credentials?
Is the author an academic based at a university or is she cited by other scholars?
Does the article include footnote references or a bibliography?
Look for the referee icon to identify peer-reviewed journals.