A 301 is a search engine friendly redirect method that basically tells the search engine that the page has been permanently moved to a different location. This technique, when used properly can be very beneficial in regards to rankings. For example if you have a page called library.html. Down the road you decide to create a replacement page called libraries.html and delete library.html. By deleting library.html, anyone who visits that old page will get a 404 file not found error, this would include search engine spiders. This will hurt your ranking if they determine that you have non-function pages or links.
If you choose to leave library.html online, you may run into another issue in regards to duplicate content. By having content that is the same on two pages, it seems to the search engine crawler that you are trying to trick it, which will result in a loss or even a ban in search engine rankings.
Another bad solution would be to use a META-refresh to refresh the user to the new page. This will prevent a 404 error, but will not tell the search engines that the page has been replaced. Some sites have been banned because of this method, mainly because it is a method used to trick search engines into giving a higher ranking.
The solution is simple: use a 301 redirect to automatically redirect anyone accessing the old page to the new page. This will also tell search engines to forget about the old page and focus more on the new page.
For more information on how to implement 301 redirects check out webconfs.com.