Selecting to "Read Online" allows you immediate access to the text from your device.
Downloading an eBook is similar to checking out a physical book: the downloaded PDF will be available on a device for a limited time before it is "returned" to the library. This is more useful if you will need to read the eBook without internet access.
For eBooks with EPUB files, you will need to install Adobe Digital Editions (it's free!). This allows you to borrow and read eBooks in EPUB formats (recommended for mobile devices).