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).
See this example, from Science magazine, Visual language discrimination in infancy. Science, 316(5828), 1159 . (In this case, Cornell Library appears in tiny letters near the top of the page. In many cases, you won't see any Cornell library branding).
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.
In addition, when you are searching the web off-campus, Google won't see the Cornell IP and you won't have the same access (see Passkey).
What can you do?