Ebook Central ebooks (formerly called EBL) are the only books the library currently maintains that need to be "checked out;" EBook Central ebooks can be checked out for up to 7 days. Other ebooks that can only be used online can be used at any time, as long as you remain online. If a publisher allows downloading as PDFs, you may use that content as long as you need it.
The chart on the main E-book FAQs page details specifics about what users are allowed to do with ebooks from particular vendors/publishers.
Some ebooks are limited to only one user at a time; in these cases, you may get a message that states that the book is in use and that you should try back later. If this happens, you should return later and try getting in again.