Solution 1:

In short, it lets you access your mail on a remote server. It does not download the mail to the local client so that any changes made on any client are reflected on the server and therefore globally accessible. This is useful for people who check mail on multiple devices. See IMAP on Wikipedia for more details.

IMAP+ or IMAPX is just evolution's better management of the IMAP protocol with their client. You can read here and here for information about what is different.

Solution 2:

I had been working for a while on improving the imap support in evolution. Took the imapx provider which was written by Michael Zuchhi (aka Notzed) and getting it ready for replacing the existing IMAP provider. To summarize what is present,

  • Fetch messages in batches
  • Fetch messages with large attachments in multiple pieces
  • IDLE support (push mail for imap)
  • All operations on messages
  • Cancel operations

The items which am working on are,

  • Store operations (folder delete/create etc.)
  • Preference options
  • Connection manager to allow concurrent folder access (configurable one)
  • Smart background message caching
  • Mutliple namespace support

Source (with video)