Could you please ellaborate the issue. What exactly happens when you try to download it? Which epub reader do you use?
Try downloading Blurfire Reader from App Store and check the same.
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[Moved the discussion to Digital Editions Forum]
There are two routes to getting epub books on ipad: direct or via PC/Mac.
For direct download, there is an Overdrive app for library books, and apps from most major vendors for their books.
(Also for Kindle books, which don't use .epub format at all).
For going via PC/Mac with Adobe DRM books you will need ADE on the PC and Bluefire app (mentioned above) or similar on the iPad.
Make sure you register Bluefire with the same AdobeID you use on the PC.
Use ADE to get the book, and to use the .acsm file to download a .epub file to the PC.
Apple likes to make life difficult, so you can't transfer the file to the ipad using file manager or similar.
You need to transfer the .epub file using something like Dropbox, iTunes or email to yourself.
With Dropbox (the most convenient for me) it will arrive on Dropbox at the ipad saying Dropbox can't open it.
However, there is a dropdown at the top right which should give an option to open with Bluefire.
You can use the same route via PC/Mac and ADE for non-DRM books.
For non-DRM books you also have the option to go via Calibre rather than ADE,
or even just to download the .epub to the PC and not to use any eBook software on the PC at all.
You will still need Dropbox or ... to transfer from PC to iPad.