The library or the web?
There are things freely available on the web that you won't find in the library. IGOs (International Governmental Organizations) and NGO's (non-governmental organizations) and other agencies post reports and data to the web. "Open Access" journals post journal articles to the web,Google Books may have a preview (or sometimes the full book) of an ebook that the library doesn't have, and, of course, there are some fairly amazing academic project websites!
On the other hand, there's a huge amount of material that is not freely available on the web, that is only available through the print and online resources the library purchases -- books, ebooks, e-journals, data sources, government documents, primary source materials, streaming media, and more. The library catalog and databases also offer ways to refine and filter your search that are not available in any web search engine.
Experienced researchers use both tools, and go back and forth between the two. Use the links on this guide to learn more about finding materials in the library's collections.